Question

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

Answer 1

The value of the side of cube is 15 cm and the decrease in volume is 1647 cm^3.

Step-by-step explanation:

Let the  side of cube be 'a'. So, volume will be { a }^{ 3 }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 = 15 cm

• If the side was decreased by 20%, then side 'a' = 12 cm.  

• The corresponding volume will be 12 x 12 x 12 = 1728 cm^3

• Decrease = 15 x 15 x 15 - 12 x 12 x 12 = 3375 - 1728 = 1647 cm^3

Thus the value of the side of cube is 15 cm and the decrease in volume is

1647 cm^3

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