RS Aggarwal solution class 8 chapter 20 Volume and Surface Area of Solid Test Paper 20

Test Paper 20

Page-231

Question 1:

Find the volume of a cube whose total surface area is 384 cm2.

Sol :

Total surface area=6a2
6a2=384
a=3846=8 cm
 Volume=a3=512 cm3

Question 2:

How many soap cakes each measuring 7 cm × 5 cm × 2.5 cm can be placed in a box of size 56 cm × 40 cm × 25 cm?

Sol :

Volume of a soap cake =7×5×2.5=87.5 cm3
Volume of the box=56×40×25=56000 cm3

No. of soap cakes=5600087.5=640 units

∴ 640 cakes of soap can be placed in a box of the given size.

Question 3:

The radius and height of a cylinder are in the ratio 5 : 7 and its volume is 550 cm3. Find its radius and height.

Sol :

Radiusheight=rh=57r=57h
Now, volume=πr2h=227×57h×57h×h=550 cm3
 h=550×7×7×722×5×53=7 cmAlso, r=57h=5 cm

Question 4:

Find the number of coins, 1.5 cm in diameter and 0.2 cm thick, to be melted to form a right circular cylinder with a height of 10 cm and a diameter of 4.5 cm.

Sol :

Volume of the coin=πr2h=227×0.75×0.75×0.2
Volume of the cylinder =πr2h=227×2.25×2.25×10
No. of coins=volume of cylinder

volume of coin=2.25×2.25×100.75×0.75×0.2= 450 coins

∴ 450 coins must be melted to form the required cylinder.

Question 5:

Find the surface area of a chalk box, whose length, breadth and height are 18 cm, 10 cm and 8 cm respectively.

Answer 5:

Length = 18 cm
Breadth = 10 cm
Height = 8 cm
∴ Total surface area =2lb+lh+bh

=218×10+18×8+10×8

=2180+144+80=808 cm2  

Question 6:

The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. Find the diameter and height of the pillar.

Sol :

Curved surface area =2πrh=264 m2
 r=2642πh=132πhm

Volume =πr2h=π×132πh×132πh×h=924 m3
 h=132×132×722×924=6 m

Now, r=132πh=132×722×6=7m

i.e., diameter of the pillar, d=7×2=14 m

Question 7:

Mark (✓) against the correct answer:
The circumference of the circular base of a cylinder is 44 cm and its height is 15 cm. The volume of the cylinder is
(a) 1155 cm3
(b) 2310 cm3
(c) 770 cm3
(d) 1540 cm3

Sol :

(b) 2310 cm3

Height = 15 cm
Circumference=2πr=44 cm
 r=44×72×22=7 cm
∴ Volume=πr2h=227×7×7×15=2310 cm3

Question 8:

Mark (✓) against the correct answer:
the area of the base of a circular cylinder is 35 cm2 and its height is 8 cm. The volume of the cylinder is
(a) 140 cm3
(b) 280 cm3
(c) 420 cm3
(d) 210 cm3

Sol :

(b) 280 cm3
Area = 35 cm2
Height = 8 cm
 Volume = base area × height = 35×8=280 cm3

Question 9:

Mark (✓) against the correct answer:
A cuboid having dimensions 16 m × 11 m × 8 m is melted to form a cylinder of radius 4 m. What is the height of the cylinder?
(a) 28 m
(b) 14 m
(c) 21 m
(d) 32 m

Sol :

(a) 28 m 
Volume of the cuboid=16×11×8=1408 m3
​Volume of the cylinder =πr2h=1408 m3
 h=1408×722×4×4=28 m

Question 10:

Mark (✓) against the correct answer:
The dimensions of a cuboid are 8 m  6 m  4 m. Its lateral surface area is
(a) 210 m2
(b) 105 m2
(c) 160 m2
(d) 240 m2

Sol :

Lateral surface area =2l+b×h=28+6×4=256=112 m2

Question 11:

Mark (✓) against the correct answer:
The length, breadth and height of a cuboid are in the ratio 3 : 4 : 6 and its volume is 576 cm3. The whole surface area of the cuboid is
(a) 216 cm2
(b) 324 cm2
(c) 432 cm2
(d) 460 cm2

Sol :

(c) 432 sq cm
Volume=lbh=3x×4x×6x=72x3 =576 cm3
x=576723=2
∴ Total surface area=2lb+bh+lh

=2(3x4x+4x6x+3x6x)

=2(48+96+72)=432 cm2

Question 12:

Mark (✓) against the correct answer:
The surface area of a cube is 384 cm2. Its volume is
(a) 512 cm3
(b) 256 cm3
(c) 384 cm3
(d) 320 cm3

Sol :

(a) 512 cm3
Surface area=6a2
6a2=384
a=3846=64=8 cm
∴ Volume=a3=83=512 cm3

Question 13:

Fill in the blanks.
(i) If l, b, h be the length, breadth and height of a cuboid, then its whole surface area = (.......) sq units.
(ii) If l, b, h be the length, breadth and height of a cuboid, then its lateral surface area = (.......) sq units.
(iii) If each side of a cube is a, then its lateral surface area is ....... sq units.
(iv) If r is the radius of the base and h be the height of a cylinder, then its volume is (.......) cubic units.
(v) If r is the radius of the base and h be the height of a cylinder, then its lateral surface area is (......) sq units.

Sol :

(i) If l, b and h are the length, breadth and height of a cuboid, respectively, then its whole surface area is equal to 2(lb+lh+bh) sq units.
(ii) If l, b and h are the length, breadth and height of a cuboid, respectively, then its lateral surface area is equal to 2((l+b)×h) sq units.
(iii) If each side of a cube is a, then the lateral surface area is 4a2 sq units.
(iv) If r and h are the radius of the base and height of a cylinder, respectively, then its volume is πr2h cubic units.
(v) If r and h are the radius of the base and height of a cylinder, then its lateral surface area is 2πrh sq units.

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