Formula :
Volume of a cube = a^{3} cubic units
Problem 1 :
Find the volume of a cube each of whose side is (i) 5 cm (ii) 3.5 m (iii) 21 cm
Solution :
(i) 5 cm :
Volume of cube = a^{3}
= 5^{3}
= 125 cm^{3}
(ii) 3.5 m :
= 3.5^{3}
= 42.875 cm^{3}
(iii) 21 cm :
= 21^{3}
= 9261 cm^{3}
Problem 2 :
A cubical milk tank can hold 125000 liters of milk. Find the length of its side in meters.
Solution :
Volume of cubical milk tank = 125000 liters
1000 liters = 1 m^{3},
Volume of tank = 125000/1000
a^{3} = 125
a = 5 m
Problem 3 :
A metallic cube with side 15 cm is melted and formed into a cuboid. If the length and height of the cuboid is 25 cm and 9 cm respectively then find the with of the cuboid.
Solution :
volume of cuboid = volume of cube
l x w x h = a^{3}
25 x w x 9 = 15^{3}
225w = 3375
Divide each side by 225.
w = 15 cm
Problem 4 :
The sides of two cubes A and B are in the ratio 3 : 5. If the volume of cube A is 729 cm^{3}, find the volume of cube B.
Solution :
From the ratio 3 : 5, the sides of cubes A and B are
3x, 5x
Volume of cube A = 243 cm^{3}
(3x)^{3} = 729
27x^{3} = 729
Divide each side by 27.
x^{3} = 27
x^{3} = 3^{3}
x = 3
Side of cube A = 3(3) = 9 cm
Side of cube B = 5(3) = 15 cm
Volume of cube B :
= 15^{3}
= 3375 cm^{3}
Problem 5 :
If the sides of two cubes are in the ratio 4 : 7, find the ratio of their volumes.
Solution :
From the ratio 4 : 7, the sides of two cubes are
4x, 7x
Ratio of their volumes :
= (4x)^{3} : (7x)^{3}
= 64x^{3} : 343x^{3}
Divide both the terms of the ratio by x^{3}.
= 64 : 343
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