Question

if the edge of the cube increased by 20% . then find the percentage increased in its volume

Answer 1

Hi ,

Let the edge of the cube = a = 10 units

Volume ( v ) = a³

v = ( 10 )³

v = 1000 cubic units ----( 1 )

If edge is increased by 20% then

edge of the new cube = s = 12units

Volume ( V ) = ( 12 )³ cubic units---( 2 )

Difference = V - v

= ( 12 )³ - ( 10)³

= ( 12 - 10 ) [ 12² + 120 + 100 ]

= 2 × 364

= 728 cubic units

Increase in volume is

1000 cubic units = 728 cubic units

100 cubic units ------x cubic units

x = ( 728 × 100 ) / 1000

x = 72.8 %

Increased percentage = x = 72.8%

I hope this helps you.

:)

Answer 2

let the edge be a

volume=a3 (cube)

20%of a =1/5a

Increased egde bg 20%=1/5a +a=6/5a


change in volume =6/5a-a=a3/5


Change of volume %=a3/5/a3×100=20%