Exercise 12E
Question 1
Find the volume of each of the following cuboids
(a)
Volume=l×b×h
=6×4×5=120cm3
(b)
Volume=l×b×h
=7×7×10=490cm3
(c)
Volume=l×b×h
=11×8×2=176cm3
(d)
Volume=l×b×h
=3×2×9=54cm3
Question 2
Find the volume of each of the following cuboids
(a) Length =12 cm, width =7 cm, height =8 cm
Sol :
(a)
Length=12cm, Width=7cm , Height=8cm
(b) Length =16 cm, width =16 cm, height =10 cm
Sol :
(b)
Length=16cm, Width=16cm , Height=10cm
(c) Length =3.5 m, width =2.8 m, height =2 m
Sol :
(c)
Length=3.5m, Width=2.8m , Height=2m
Question 3
Find the volume of each cube of side length:
(a) 5 cm
(b) 8 cm
(c) 0.3 m
(d) 50 mm
(e) 1.2 m
Sol :
Question 4
A cuboidal water tank is 7 m long, 5 m width and 4 m deep. How many litres of water can it hold?
Sol :
Tank can hold water= l×b×h
=7×5×4=140 m3
∵1m3=1000l
multiplying both side by 140
(140×1) m3=(140×1000) l
Question 5
A cuboidal tank is 12 m long and 8 m wide. What should be its height so that it may hold $960 \mathrm{~m}^{3}$ of water?
Sol :
Length of tank=l=12m
Width of tank=8m
ATQ,
l×w×h=960
$h=\frac{960}{l\times w}=\frac{960}{12\times 8}$
=10 m
Question 6
A solid cube of side 12 cm is cut into eight cubes of equal volume. Calculate the size of the new cube.
Sol :
=1728 cm3
∴Large cube is cut into 8 cube
∴Small cube volume$=\frac{1728}{8}$
=216 cm3
Question 7
A cube of side length 8 cm is immersed completely in a rectangular vessel containing water. If the base is 16 cm long and 10 cm wide, then, find the rise in water level in the vessel.
Sol :
=512cm3
The water level rise due to immerse of cube.
∴Rise in water level= h cm
The volume of water rise is equal to volume of the cube.
∴Volume of water rise=16×10×h=512
$h=\frac{512}{16\times 10}$
=3.2cm
∴Water level rise=3.2cm
Question 8
A godown is in the form of a cuboid measuring 40 m by 30 m by 20 m. How many cuboidal boxes of volume $1.2 \mathrm{~m}^{3}$ each can be stored in the godown?
Sol :
Volume of godown=40×30×30=24000m3
1.2m3 of volume need=1 cuboidal box
∴24000m3 of volume needed$=\frac{24000}{1.2}$
$=\frac{240000}{12}=20000$
∴Number of cuboidal box=20000
Question 9
A machine for making ice bricks freezes 5.76 litres of water into ice cubes measuring 4 cm by 3 cm by 2 cm. How many ice bricks will be made?
Sol :
We know that:-
1litre=1000cm3
∴5.76litre=5.76×1000=5760cm3
∴Volume of Ice cubes=4×3×2=24cm3
∴Ice bricks will be made$=\frac{5760}{24}=240$
Question 10
A storage tank at a petrol station is a cuboid 4 m long , 3 m wide and 2 m deep. In one day if the station sells 7200 litres of petrol from the tank, what is the fall in the level of the petrol in the tank?
Sol :
We know that:-
1Litre=0.001m3
∴7200litre=7200×0.001$=\frac{7200}{1000}$=7.2m3
Let , the fall level=x m
∴ATQ,
4×3×2=7.2
12x=7.2
$x=\frac{7.2}{12}$=0.6m
=60cm or 0.6 m
Question 11
The platform at the base of a statue is to be built to a height of 1.5 m on a square base measuring 2 m by 2 m. It is to be constructed from bricks of dimensions 25 cm, 15 cm and 10 cm. How many bricks will be required to build the base of the statue?
Sol :
∵1m=100 cm
∴2m=200 cm and 1.5m=150 cm
Single brick dimension=25×15×10cm
=3750cm3
∴Brick needed$=\frac{6000000}{3750}$
=1600
Question 12
On a certain day 8 cm of rain fell. Calculate the volume of water that fell on 1.8 ha of land.
Sol :
∴Depth of water on the land=8cm or 0.08m
We know that:-
1h=10000m2
1.8h=10000×1.8=18000m2
∴Volume of water=0.08×18000=1440m3
Question 13
A covered wooden box has the inner measure as 115 cm, 75 cm and 35 cm and the thickness of wood is 2.5 cm. Find the volume of the wood.
Sol :
Question 14
Each side of a cube is decreased by 25% . Find the ratio of the volume of the original cube and the resulting cube.
Sol :
Question 15
100 men took a dip in a pond 50 m long and 18 m wide. If the average displacement of water by a man was 3.6m3 , then calculate the rise in the water level.
Sol :
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