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  • 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 length of each side of it is reduced by 20%?

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 length of each side of it is reduced by 20%?

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When length of each side of a cube is increased by 3 cm, its volume is increased by 2457

(a+3)^3-a^3=2457;;;;;;(ecause Volume;of ;cube=a^3)

a^3+3^3+3 imes a^2 imes (3)+3 imes a imes 3^2-a^3=2457

27+9 imes a^2+27 imes a=2457

a^2+3a-270=0

a^2+18a-15a-270=0

a(a+18)-15(a+18)=0

(a-15)(a+18)=0

a=(-18) ;;;;not possible

So, a=15;cm

If side reduced by 20% then  it becomes 12 cm 

then volume reduced by 

=15^3-12^3=3375-1728=1647 cm^3

Posted by

Deependra Verma

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