Question

When the length of each side of a cube is increased by 3 cm, its volume is increased by 2457 cm³. Find its side. How much will its volume decrease, if the length of each side of it is reduced by 20%?

Answer 1

Let a be the side of the cube.
Side of the new cube = a + 3
Volume of the new cube = a³ + 2457
That is, ( a + 3 )³ = a³ + 2457
⇒ a³ + 3 x a x 3 ( a + 3 ) + 3³ = a³ + 2457
⇒ 9a² + 27a + 27 = 2457
⇒ 9a² + 27a - 2430 = 0
⇒ a² + 3a - 270 = 0
⇒ a ( a + 18 ) - 15 ( a + 18 ) = 0
⇒ ( a - 15 ) ( a + 18 ) = 0
⇒ a - 15 = 0 or a + 18 = 0
⇒ a = 15  or a = - 18
⇒ a = 15 cm  ...[ since side cannot be negative ] 

Volume of the cube whose side is 15 cm = 15³ = 3375 cm³ 

Suppose the length of the given cube is reduced by 20%.
Thus new side a new = a - `20 / 100` x a

                                   = `a ( 1 - 1/5)`

                                   = ` 4/5` x 15

                                    =  12 cm

Volume of the new cube whose side is 12 cm = 12³ = 1728 cm³
Decrease in volume = 3375 - 1728 = 1647 cm³