myhelper: Volume and Surface Area of Solids

Showing posts with label Volume and Surface Area of Solids. Show all posts

S.chand Class 8 Maths Solution Chapter 17 Volume and Surface Area of Solids Exercise 17 E

Exercise 17 E

Question 1

Copy and complete the table $\left(\pi=\frac{22}{7}\right)$

	(a)	(b)	(c)
Radius of the circle (cm)	7	14	21
Height (cm)	8	16	40
Volume $(cm^3)$	?	?	?

2. The volume of a cylinder is $660 \mathrm{~cm}^{3}$. Find its height if its radius is $5 \mathrm{~cm}$.

3. The volume of a cylinder is $448 \pi \mathrm{cm}^{3}$ and height $7 \mathrm{~cm}$. Find its lateral (curved) surface area and total surface area.

4. The volume of a right circular cylinder is $1100 \mathrm{~cm}^{3}$ and the radius of its base is $5 \mathrm{~cm}$. Find its curved surface area. ( $\pi=22 / 7)$

5. A solid cylinder has total surface area of $462 \mathrm{sq} \mathrm{cm}$. Its curved area is one third of its total surface area. Find the volume of the cylinder. (Take $\left.\pi=\frac{22}{7}\right)$

6. If base radius of a right circular cylinder is halved, keeping the height same, find the ratio of the volume of the reduced cylinder to that of the original cylinder.

7. A cylindrical tank has a capacity of $6160 \mathrm{cu} \mathrm{cm}$. Find its depth if its radius is $14 \mathrm{~cm}$. Calculate the cost of painting its curved outer surface at the rate of $₹ 3$ per sq $\mathrm{cm}$. (Take $\left.\pi=\frac{22}{7}\right)$

8. The circumference of the base of a cylindrical vessel is $132 \mathrm{~cm}$ and its height is $25 \mathrm{~cm}$. How many litres of water can it hold ?

9. A hollow cylindrical tube open at both ends is made of iron $3 \mathrm{~cm}$ thick. If the external diameter be $56 \mathrm{~cm}$ and the length of the tube be $182 \mathrm{~cm}$, find the number of cubic $\mathrm{cm}$ in it.

10. A well $14 \mathrm{~m}$ inside diameter is dug $15 \mathrm{~m}$ deep. Earth taken out is spread all around to a width of $7 \mathrm{~m}$ to form an embankment. Find the height of the embankment.

11. The rain falls $10 \mathrm{~cm}$ on a particular day. The rain water that falls on a roof $70 \mathrm{~m}$ long and $44 \mathrm{~m}$ wide was collected in a cylindrical tank of radius $14 \mathrm{~m}$. Find

(i) volume of the water that falls on the roof.

(ii) rise of water level in the tank due to rain water.

[Hint. Volume of rain water $=l \times b \times h=70 \times 44 \times \frac{1}{10}=308 \mathrm{~m}^{3}$

Let $h \mathrm{~m}$ be the rise in water level. Then volume of the cylindrical column of water of height $h=$ volume of rain water) i.e., $\pi \times 14^{2} \times h=308$. ]

Multiple Choice Questions (MCQs)

12. The curved surface of a cylindrical pillar is $264 \mathrm{~m}^{2}$ and its volume is $924 \mathrm{~m}^{3}$. The diameter of the pillar is

(a) $5 \mathrm{~m}$

(b) $9 \mathrm{~m}$

(d) $14 \mathrm{~m}$

13. The radii of two cylinders are in the ratio 2: 3 and their heights are in the ratio $5: 3$. The ratio of their volumes is

(a) $27: 20$

(b) $20: 27$

(d) $9: 4$

S.chand Class 8 Maths Solution Chapter 17 Volume and Surface Area of Solids Exercise 17 D

Exercise 17 D

Question 1

1. Information about a few cylinders is given below. Copy and complete the table. $\left(\pi=\frac{22}{7}\right)$

	Radius (cm)	Height (cm)	Curved Surface	Area of the base	Whole surface
(a)	7	6
(b)	14	10
(c)	21	5
(d)	$10 \frac{1}{2}$	16

2. Copy and complete the table. $\left(\pi=\frac{22}{7}\right)$.

	(a)	(b)	(c)	(d)
Curved Surface $(cm^2)$	704	3960	1320	24200
Radius (cm)	?	15	?	35
Height (cm)	8	?	14	?

In the following problems, take $\pi=\frac{22}{7}$ if not mentioned otherwise.

3. The circumference of the base of a right circular cylinder is $220 \mathrm{~cm}$. If the height of the cylinder is $2 \mathrm{~m}$, find the lateral surface area of the cylinder.

4. Aclosed circular cylinder has diameter $20 \mathrm{~cm}$ and height $30 \mathrm{~cm}$. Find the total surface area of the cylinder. $(\pi=3.14)$

5. A cylindrical pillar is $1 \mathrm{~m}$ in diameter and $4.2 \mathrm{~m}$ in height. Find the cost of white washing the curved surface of the pillar at the rate of $₹ 15$ per $\mathrm{m}^{2}$.

6. Find the height of the solid circular cylinder of total surface area $660 \mathrm{~cm}^{2}$ and radius $5 \mathrm{~cm}$.

[Hint. $2 \pi r^{2}+2 \pi r h=660 \Rightarrow 2 \pi r(r+h)=660$

$\left.\Rightarrow 2 \times \frac{22}{7} \times 5 \times(5+h)=660 \Rightarrow 5+h=\frac{660 \times 7}{2 \times 22 \times 5}=21\right]$

7. The inner diameter of a circular well is $4.2 \mathrm{~m}$. It is $12 \mathrm{~m}$ deep. Find (i) its inner curved surface area (ii) the cost of plastering the inner curved surface at the rate of $₹ 50$ per $\mathrm{m}^{2}$.

8. A metal pipe is $77 \mathrm{~cm}$ long, the inner diameter of the cross-section is $4 \mathrm{~cm}$ and the outer diameter is $4.8 \mathrm{~cm}$. Find the (i) inner curved surface area (ii) outer curved surface area (iii) total surface area.

9. A hollow cylindrical pipe has inner circumference $44 \mathrm{dm}$ and outer $45 \mathrm{dm}$. Find the cost of painting it from both sides (inside as well as outside) at $₹ 2$ per $\mathrm{m}^{2}$ if length is $3.5 \mathrm{~m}$.

S.chand Class 8 Maths Solution Chapter 17 Volume and Surface Area of Solids Exercise 17 C

Exercise 17 C

Question 1

1. A solid cube of edge $20 \mathrm{~cm}$ is melted and cast into a cuboid whose base measures $25 \mathrm{~cm}$ by $20 \mathrm{~cm}$. Find the height of the cuboid.

2. A rectangular block of metal measuring $4 \mathrm{~cm}$ by $5 \mathrm{~cm}$ by $6 \mathrm{~cm}$ was melted down to make a block $8 \mathrm{~cm}$ long by $3 \mathrm{~cm}$ wide. How high was the block ?

3. How many bricks, each of dimensions $25 \mathrm{~cm} \times 16 \mathrm{~cm} \times 10 \mathrm{~cm}$ will be needed to build a wall $24 \mathrm{~m}$ long, $6 \mathrm{~m}$ high and $0.4 \mathrm{~m}$ thick.

4. The inside measurements of a cardboard box are $1 \frac{1}{2} \mathrm{~m}$ by $\frac{3}{4} \mathrm{~m}$ by $60 \mathrm{~cm}$. How many books, $20 \mathrm{~cm}$ by $10 \mathrm{~cm}$ by $7.5 \mathrm{~cm}$ each can be arranged in the box ?

5. A class room is $12 \mathrm{~m}$ long, $5 \mathrm{~m}$ wide and $3 \mathrm{~m}$ high. How many pupils should it be used for if each pupil required $5 \mathrm{~m}^{3}$ of air space ?

6. How many lead cubes of side $2 \mathrm{~cm}$ could be made from a lead cube of side $8 \mathrm{~cm}$ ?

7. How many wooden cubical blocks of edge $20 \mathrm{~cm}$ can be cut from a log of wood of size $8 \mathrm{~m}$ by $5 \mathrm{~m}$ by $80 \mathrm{~cm}$, assuming there is no wastage.

8. A cuboid of dimensions $10 \mathrm{~cm}$ by $2 \mathrm{~cm}$ by $2 \mathrm{~cm}$ is divided into 5 cubes of edge $2 \mathrm{~cm}$. Find the ratio of the total surface area of the cuboid and that of the cubes.

9. A pit $5 \mathrm{~m}$ long and $3.5 \mathrm{~m}$ wide is dug to a certain depth. If the volume of earth taken out of it is $14 \mathrm{~m}^{3}$, what is the depth of the pit ?

10. The dimensions of a field are $15 \mathrm{~m}$ by $12 \mathrm{~m}$. A pit $7.5 \mathrm{~m}$ long, $6 \mathrm{~m}$ wide and $1.5 \mathrm{~m}$ deep is dug at one corner of the field. The earth removed is evenly spread over the remaining area of the field. Calculate the rise in the level of the field.

Multiple Choice Questions (MCQs)

11. How many bricks, each measuring $25 \mathrm{~cm} \times$ $11.25 \mathrm{~cm} \times 6 \mathrm{~cm}$ will be needed to build a wall $8 \mathrm{~m} \times 6 \mathrm{~m} \times 22.5 \mathrm{~cm}$.

(a) 5600

(b) 6000

(d) 7200

12. A cube of lead with edges measuring $6 \mathrm{~cm}$ each is melted and formed into 27 equal cubes. What will be the length of the edges of the new cubes?

(a) $3 \mathrm{~cm}$

(b) $4 \mathrm{~cm}$

(d) None of these

S.chand Class 8 Maths Solution Chapter 17 Volume and Surface Area of Solids Exercise 17 B

Exercise 17 B

Question 1

1. Work out the volume of each cuboid.

<fig>

2. Find the volume of each of the following cuboids:

	Length	Breadth	Height
(a)	5 cm	5 cm	4 cm
(b)	45 mm	30 mm	10 mm
(c)	12 cm	1.2 cm	0.5 cm
(d)	1.2 m	0.9 m	0.7 cm

3. Complete the table: Measurements are in cm

	(i)	(ii)	(iii)	(iv)	(v)	(vi)
Length	4	12	16	?	40	60
Breadth	3	9	14	28	24	?
Height	5	12	18	24	?	5
Volume	?	?	?	26208	2400	5400

4. Find the volume of a cube with the given side :

(a) $3 \mathrm{~cm}$

(b) $\frac{1}{5} \mathrm{~cm}$

(d) $2.5 \mathrm{~m}$

5. Find each edge of the cubes whose volumes are :

(a) $216 \mathrm{~m}^{3}$

(b) $512 \mathrm{~cm}^{3}$

(d) $2197 \mathrm{~m}^{3}$

6. Find the volume of air in a room measuring $4 \mathrm{~m}$ by $5 \mathrm{~m}$ which is $3 \mathrm{~m}$ high.

7. Which has the greater volume : a box that measures $10 \mathrm{~cm}$ by $6 \mathrm{~cm}$ by $4 \mathrm{~cm}$ or one that measures $6 \mathrm{~cm}$ by $6 \mathrm{~cm}$ by $7 \mathrm{~cm}$ ?

8. The bottom of a tank measures $25 \mathrm{~m} \times 20 \mathrm{~m}$. Find its depth if it contains $2000 \mathrm{~m}^{3}$ water.

9. Find the volume of a cube, one face of which has an area of $64 \mathrm{~cm}^{2}$.

10. A heap of wood is a pile $5 \mathrm{dm}$ wide, $9 \mathrm{dm}$ long, and $3 \mathrm{dm}$ high. What is the volume of the heap of wood?

11. The volume of a soap cake is $160 \mathrm{~cm}^{3}$. Its length and width are $10 \mathrm{~cm}$ and $5 \mathrm{~cm}$. Find its height.

12. If $60 \mathrm{~cm}^{3}$ of a metal weighs $1 \mathrm{~kg}$, find the weight of a block of the same metal of the size $20 \mathrm{~cm}$ by 12 cm by $5 \mathrm{~cm}$.

13. In a shower, $5 \mathrm{~cm}$ of rain falls. Find the volume of water that falls on 2 hectares of land.

14. A river 2 metres deep and 45 metres wide is flowing at the rate of $3 \mathrm{~km}$ per hour. Find the amount of water that runs into the sea per minute.

15. A beam $9 \mathrm{~m}$ long, $50 \mathrm{~cm}$ wide, and $20 \mathrm{~cm}$ deep is made of wood which weighs $30 \mathrm{~kg}$ per $\mathrm{m}^{3}$, find the weight of the beam.

16. A wooden box (including the lid) has external dimensions of $40 \mathrm{~cm}$ by $34 \mathrm{~cm}$ by $30 \mathrm{~cm}$. If the wood is $1 \mathrm{~cm}$ thick, how many $\mathrm{cm}^{3}$ of wood are there in it?

17. The outer dimensions of a closed wooden box are $10 \mathrm{~cm}$ by $8 \mathrm{~cm}$ by $7 \mathrm{~cm}$. Thickness of the wood is 1 $\mathrm{cm}$. Find the total cost of wood required to make the box if $1 \mathrm{~cm}^{3}$ of wood costs $₹ 2.00$.

18. 500 men took dip in a tank which is $80 \mathrm{~m}$ long, $50 \mathrm{~m}$ broad. What is the rise in water level if the average displacement of water by a man is $4 \mathrm{~m}^{3}$ ?

[Hint. Volume of water displaced by 500 men $=(4 \times 500)=2000 \mathrm{~m}^{3}$

Area of the tank $=80 \times 50=4000 \mathrm{~m}^{2}$. Let the rise in the level of water $=h$ metres. Then $4000 \times h=2000$ ]

Multiple Choice Questions (MCQs)

19. The three co-terminous edges of a cuboid are 36,75 and $80 \mathrm{~cm}$ respectively. The edge of the cube of the same volume will be :

(a) $60 \mathrm{~cm}$

(b) $55 \mathrm{~cm}$

(d) $65 \mathrm{~cm}$

20. If the volume of a cube is $729 \mathrm{~cm}^{3}$, then its surface area will be

(a) $486 \mathrm{~cm}^{2}$

(b) $476 \mathrm{~cm}^{2}$

(d) $456 \mathrm{~cm}^{2}$

S.chand Class 8 Maths Solution Chapter 17 Volume and Surface Area of Solids Exercise 17 A

Exercise 17 A

Question 1

Find the surface area of each of the cuboids whose dimensions are given below:

	(i)	(ii)	(iii)	(iv)	(v)	(vi)
l	5 cm	6 cm	10 cm	4 cm	$5 \frac{1}{2}$ cm	16 cm
b	4 cm	3 m	8 cm	1.7 cm	4 cm	8 cm
h	3 cm	2 m	5 cm	2.3 cm	$10 \frac{1}{2}$ cm	6 cm

2. Find the surface area of the following cubes :

(a) $l=8 \mathrm{~cm}$

(b) $l=12 \mathrm{~cm}$

(d) $l=5 \mathrm{dm}$

(e) $l=1.2 \mathrm{~m}$

(f) $l=2.25 \mathrm{~m}$

3. The total surface area of a cube is $54 \mathrm{~cm}^{2}$. What is the length of its sides ?

4. Find the surface area of a wooden box which is in the shape of a cube, if the edge of the box is $27 \mathrm{~cm}$.

5. Find the cost of painting the all round outer surface of a box with lid $60 \mathrm{~cm}$ long, $40 \mathrm{~cm}$ wide and $30 \mathrm{~cm}$ high at 50 p per $20 \mathrm{~cm}^{2}$.

6. The dimensions of an oil tin are $26 \mathrm{~cm} \times 26 \mathrm{~cm} \times 45 \mathrm{~cm}$. Find the area of the tin sheet required for making 20 such tins. If $1 \mathrm{sq} \mathrm{m}$ of the tin sheet costs $₹ 10$, find the cost of tin used for these 20 tins.

7. Find the area of the thin sheeting required for making an open cistern (i.e., without a lid), $5 \mathrm{~m}$ long, $3 \mathrm{~m}$ wide, $4 \mathrm{~m}$ deep.

8. A swimming pool is $20 \mathrm{~m}$ in length, $15 \mathrm{~m}$ in breadth, and $4 \mathrm{~m}$ in depth. Find the cost of cementing its floor and walls at the rate of $₹ 12$ per square metre.

9. Two cubes, each of side $15 \mathrm{~cm}$ are joined end to end. Find the surface area of the resulting cuboid.

Multiple Choice Questions (MCQs)

10. The perimeter of one face of a cube is $20 \mathrm{~cm}$. Its total surface area is :

(a) $2400 \mathrm{~cm}^{2}$

(b) $150 \mathrm{~cm}^{2}$

(d) $96 \mathrm{~cm}^{2}$

11. A cube of edge $5 \mathrm{~cm}$ is cut into cubes, each of edge $1 \mathrm{~cm}$. The ratio of the total surface area of one of small cubes to that of the large cube is :

(a) $1: 125$

(b) $1: 5$

(d) $1: 25$

12. Find the cost of painting the four walls of a room 10 metres long, 5 metres broad and 6 metres high at the cost of $₹ 4$ per square metre.

(a) ₹ 720

(b) ₹ 880

(c)₹ 360

(d) ₹ 1200

High Order Thinking Skills (HOTS)

13. The area of the four walls in a room is $120 \mathrm{~m}^{2}$. The length of twice the breadth. If the height of the room is $4 \mathrm{~m}$, find the area of the floor.

S.chand books class 8 maths solution chapter 27 Volume and Surface Area of Solids exercise 27 C

EXERCISE 27 C

OPEN IN YOUTUBE

Question 1

Find the volume of each of the following cylinders whose:
(i) Radius of base = 10cm
Height = 14 cm

(ii) Radius of base = 21cm
Height = 30 cm

(iii) Radius of base = 10.5cm
Height = 35 cm

Sol :

OPEN IN YOUTUBE

Question 2

The area of the base of a circular cylinder is 35 cm² and its height 12 cm. What will be its volume?

Sol :

OPEN IN YOUTUBE

Question 3

If the capacity of a cylindrical tank is 1848 m3 and the diameter of the base is 14 m, then what is the depth of the tank?

Sol :

OPEN IN YOUTUBE

Question 4

If the volume of a right circular cylinder with its height equal to the radius is $25\dfrac{1}{7}~cm^3$ , then find the radius of the base of the cylinder.

Sol :

OPEN IN YOUTUBE

Question 5

Total surface area of a right circular cylinder is 1540cm² . If its height is four times the radius, then find the volume of the cylinder.

Sol :

OPEN IN YOUTUBE

Question 6

A drainage tile is a cylindrical shell 21cm long. The inside and outside diameters are 8cm and 10cm respectively . What is the volume of clay required for the tile ?

Sol :

OPEN IN YOUTUBE

Question 7

The volume of the metal of a cylindrical pipe is 748 cm³. The length of the pipe is 14 cm and the extemal radius is 9cm. What is the thickness of metal in the pipe ?

Sol :

OPEN IN YOUTUBE

Question 8

Two right circular cylinders of equal volume have their heights in the ratio 1 : 2. What is the ratio of their radii?

Sol :

OPEN IN YOUTUBE

Question 9

Water is being pumped out through a circular pipe whose internal diameter is 7 cm. If the f‌low of water is 12 cm/s. How many litres of water is being pumped out in an hour?

Sol :

OPEN IN YOUTUBE

Question 10

If a solid right circular cylinder made of iron is heated to increase its radius and height by 1% each , then by how much per cent does the volume of the solid increase ?

Sol :

We know that, if 'r' and 'h' be the radius and height of a right circular cylinder, then its volume will be

V=πr²h

Now, if radius and height are increased by 1%, then the new radius and height will be

r' h=r+1%×r

=r+0.01r=1.01r

h' =h+1%×h

=1.01h

Therefore, new volume will be

V' =πr'²h'=π(1.01r)r²(1.01h)

=1.030301πr²h

So, increase in the volume is

I=V' -V=1.030301V-V

=0.030301V

Thus, percentage of increase in volume will be
I% = 0.030301 × 100%=3.0301%.

OPEN IN YOUTUBE

Question 11

A well 20m in diameter is dug 18m deep and earth taken out is spread all around it to a width of 5m to form a embankment. What is the height of the embankment ?

Sol :

S.chand books class 8 maths solution chapter 27 Volume and Surface Area of Solids exercise 27 B

EXERCISE 27 B

Q1 | Ex-27B | Class 8| S.Chand | Composite maths |Volume and Surface Area of Solids| myhelper

OPEN IN YOUTUBE

Question 1

Copy and complete the given table for a cylinder (use pi=22/7)

	Radius	Height
(i)	14cm	20cm
(ii)	0.28cm	45cm
(iii)	5.6cm	13.2cm

Sol :

C.SA (2πrh)

(i)=2π(14)(20)
=1760cm²

(ii)=2π(0.28)(45)
=79.2cm²

(iii)=2π(5.6)(13.2)
=464.64cm²

Area of base(πr²)
(i)=π(14)²
=616cm²

(ii)=π(0.28)²
=0.2464cm²

(iii)=π(5.6)²
=98.4707cm²

Total Surface Area(=2πr(h + r))

(i)=2π(14)[20+14]

=2992cm²
(ii)=2π(0.28)[45+0.28]

=79.6928cm²
(iii)=2π(5.6)[13.2+5.6]
=661.76cm²

Q2 | Ex-27B | Class 8| S.Chand | Composite maths |Volume and Surface Area of Solids| myhelper

OPEN IN YOUTUBE

Question 2

Find the radius of a cylinder whose height is 42cm and whose curved surface area is 8448 cm².

Sol :

Q3 | Ex-27B | Class 8| S.Chand | Composite maths |Volume and Surface Area of Solids| myhelper

OPEN IN YOUTUBE

Question 3

The total surface area of a right circular cylinder of radius 7cm is 1188cm² . Find its height

Sol :

Q4 | Ex-27B | Class 8| S.Chand | Composite maths |Volume and Surface Area of Solids| myhelper

OPEN IN YOUTUBE

Question 4

Four times the area of the curved surface of a cylinder is equal to 6 times the sum of the area of its bases if its height is 14cm , find the curved surface area .

Sol :

Q5 | Ex-27B | Class 8| S.Chand | Composite maths |Volume and Surface Area of Solids| myhelper

OPEN IN YOUTUBE

Question 5

The circumference of the base of a right circular cylinder is 176cm and it is 1m high . Find the lateral surface area of the cylinder.

Sol :

Q6 | Ex-27B | Class 8| S.Chand | Composite maths |Volume and Surface Area of Solids| myhelper

OPEN IN YOUTUBE

Question 6

A cylindrical vessel open at the top has a diameter of 21cm and height 16cm. Find the cost of tin plating it on the inside at the rate of 10 rupees per hundred square centimetres.

Sol :

Q7 | Ex-27B | Class 8| S.Chand | Composite maths |Volume and Surface Area of Solids| myhelper

OPEN IN YOUTUBE

Question 7

A hollow metal pipe is 63cm long. The inner diameter of cross-section is 4cm and the outer diameter is 4.8cm. Find the total surface area of the pipe.

Sol :

S.chand books class 8 maths solution chapter 27 Volume and Surface Area of Solids exercise 27 A

EXERCISE 27 A

OPEN IN YOUTUBE

Question 1

Find the surface area and volume of cuboid whose dimensions are :

Surface Area of cuboid =2(lb+bh+hl)

Volume of cuboid $=l \times b \times h$

(i) 3m , 5m and 7m

Sol :

Volume $=3 \times 5 \times 7=105 \mathrm{~m}^{3}$

$\begin{aligned}\text { Surface Area } &=2(3 \times 5+5 \times 7+7 \times 3) \mathrm{m}^{2} \\&=2(15+35+21) \mathrm{m}^{2} \\&=(2 \times 71) \mathrm{m}^{2} \\&=142 \mathrm{~m}^{2}\end{aligned}$

(ii) 4.8m , 80cm and 50cm

Sol :

(iii) 2.4cm , 16cm , 4mm

Sol :

OPEN IN YOUTUBE

Question 2

Find the surface area and volume of a cube whose side is :
(i) 6cm
(ii) 1.2cm
(iii) $\dfrac{1}{8}~cm$

Sol :

OPEN IN YOUTUBE

Question 3

Find the volume in m³ of a rectangular cuboid of length 2.6m , width 80cm and height 500mm.

Sol :

1m=100cm

$\frac{1}{100}m=1cm$

$\frac{2.6}{100}m=2.6cm$

80cm=0.80m=b

1cm=10mm

$\frac{1}{10}cm=1mm$

$\frac{500}{10}cm=500mm$

50cm=500mm

1m=100cm

$\frac{1}{100}m=1cm$

$\frac{50}{100}m=50cm$

0.50m=50cm=h

Volume =2.6m×0.80m×0.50m

=1.04m³

OPEN IN YOUTUBE

Question 4

A rectangular trough 8m long and 3m wide holds 57.6 m³ of water. Find the depth of water in the trough.

Sol :

OPEN IN YOUTUBE

Question 5

2 litres of petrol are poured into a rectangular container 25cm long , 8cm wide and 25cm deep. What is the depth of the petrol in the container?

Sol :

Dimension of container =25cm×8cm ×25cm

2 litres of petrol=2000cm³

Volume of petrol=l×b×h

2000=25×8×x

$\frac{2000}{25\times 8}=x$

$\frac{2000}{200}=x$

x=10

Deapth=10cm

OPEN IN YOUTUBE

Question 6

The surface area of a cube is $37\dfrac{1}{2}~m^2$ . Find the volume of the cube.

Sol :

OPEN IN YOUTUBE

Question 7

Find the number of bricks each measuring 24cm by 15cm by 8cm that are needed to build a wall 33m long , 48cm wide and 2.8m high.

Sol :

OPEN IN YOUTUBE

Question 8

Find the number of 4cm cubes that can be cut out from a cuboid , whose dimensions are 32cm by 21cm by 6cm .

Sol :

OPEN IN YOUTUBE

Question 9

What is the maximum length of a pencil that can be kept in a rectangular box of dimensions 8cm by 6cm by 2cm ?

Sol :

Maximum length=2√26 cm

OPEN IN YOUTUBE

Question 10

How many litres of water can a square container of side 20cm and height 18cm hold ?

Sol :

OPEN IN YOUTUBE

Question 11

The length , breadth and height of a room are in the ratio 3 : 2 : 1. If its volume is 1296m³ , find its breadth.

Sol :

OPEN IN YOUTUBE

Question 12

What is the volume of a cube (in cm³) whose diagonal measures 4√3 cm ?

Sol :

OPEN IN YOUTUBE

Question 13

The whole surface area of a rectangular block is 8788cm² .If the length , breadth and height are in the ratio 4:3:2 , find the difference between its length and height.

Sol :

OPEN IN YOUTUBE

Question 14

Find the number of bricks each measuring 25cm by 12.5cm by 7.5 cm , required to construct a wall 12m long , 5m high and 0.25m thick, while the sand and cement mixture occupies 5% of the total volume of the wall ?

Sol :

OPEN IN YOUTUBE

Question 15

A closed rectangular box measuring 72cm by 54cm by 48cm externally is made of wood 1.5cm thick.
(i) Find the capacity(Volume) of the box in litres.
(ii) What is the volume of wood used in making the box ?
(iii) What is the mass of the box, if the wood used weighs 0.9g/cm³ ?

Sol :

OPEN IN YOUTUBE

Question 16

A rectangular plot of field measures 12m by 15m . A pit 8m by 6m by 50cm is dug in the field and soil removed is spread evenly over the remaining portions of the field. Find the increasing in the level of the remaining portion of the field .

Sol :

OPEN IN YOUTUBE

Question 17

A box is tightly packed with tins of soft drinks of same size. These tins are arranged in 2 layers contains 3 rows of 5 column as shown. If the diameter of each tin is 6cm and it is 12cm high, find the volume of the box.
[Hint: Length=6*5=30cm , Breadth=6*3=18 cm , Height=12*2 (being 2 layers) = 24cm]

Sol :

Length=6×5=30cm ,

Breadth=6×3=18 cm ,

Height=12×2 (being 2 layers) = 24cm

Volume of box=l×b×h

=30×18×24

=12960 cm³

Exercise 17 E

Question 1

Exercise 17 D

Question 1

Exercise 17 C

Question 1

Exercise 17 B

Question 1

Exercise 17 A

Question 1

EXERCISE 27 C

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

EXERCISE 27 B

Q1 | Ex-27B | Class 8| S.Chand | Composite maths |Volume and Surface Area of Solids| myhelper

Question 1

Q2 | Ex-27B | Class 8| S.Chand | Composite maths |Volume and Surface Area of Solids| myhelper

Question 2

Q3 | Ex-27B | Class 8| S.Chand | Composite maths |Volume and Surface Area of Solids| myhelper

Question 3

Q4 | Ex-27B | Class 8| S.Chand | Composite maths |Volume and Surface Area of Solids| myhelper

Question 4

Q5 | Ex-27B | Class 8| S.Chand | Composite maths |Volume and Surface Area of Solids| myhelper

Question 5

Q6 | Ex-27B | Class 8| S.Chand | Composite maths |Volume and Surface Area of Solids| myhelper

Question 6

Q7 | Ex-27B | Class 8| S.Chand | Composite maths |Volume and Surface Area of Solids| myhelper

Question 7

EXERCISE 27 A

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Contact Form