Question

If each side of a cube is reduced by 20% the volume of the cube will be reduced by

Answer 1

Answer:

Let the side of cube be 'a'. So, volume will be a

3

.

Increased side of the cube a' = a + 3. Hence the increased volume = a

3

+2457.

Increased volume of cube =

a

3

+2457=a

3

+27+9a(a+3)[(a+b)

3

=a

3

+b

3

+3aba+b)]

⟹2457=27+9a

2

+27a

⟹9a

2

+27a−2430=0

⟹a

2

+3a−270=0

⟹a

2

+18a−15a−270=0

⟹a(a+18)−15(a+18)=0

⟹a=15cm

If the side was decreased by 20%, then side

′

a

′

=12cm. The corresponding volume will be 12∗12∗12=1728 cu. cm

Decrease =15∗15∗15−12∗12∗12=3375−1728=1647 cu. cm