EXERCISE 27 A
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 :
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 :
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
$\frac{1}{100}m=1cm$
$\frac{50}{100}m=50cm$
Volume =2.6m×0.80m×0.50m
=1.04m3
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 :
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
Question 6
The surface area of a cube is $37\dfrac{1}{2}~m^2$ . Find the volume of the cube.
Sol :
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 :
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 :
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
Question 10
How many litres of water can a square container of side 20cm and height 18cm hold ?
Sol :
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 :
Question 12
What is the volume of a cube (in cm3) whose diagonal measures 4√3 cm ?
Sol :
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 :
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 :
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 :
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 :
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
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