SOLVING WORD PROBLEMS INVOLVING VOLUME OF CUBES

Formula : 

Volume of a cube = a³ 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 = a³

= 5³

= 125 cm³

(ii) 3.5 m :

= 3.5³

= 42.875 cm³

(iii) 21 cm :

= 21³

= 9261 cm³

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 m³,

Volume of tank = 125000/1000

a³ = 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 = a³

25 x w x 9 = 15³

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 cm³, 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 cm³

(3x)³ = 729

27x³ = 729

Divide each side by 27.

x³ = 27

x³ = 3³

x = 3

Side of cube A = 3(3) = 9 cm

Side of cube B = 5(3) = 15 cm

Volume of cube B : 

= 15³

= 3375 cm³

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

= 64x³ : 343x³

Divide both the terms of the ratio by x³.

= 64 : 343

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