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Question

Find the approximate change in the volume V of a cube of side x meters caused by increasing the side by 2%.

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Solution

Given that the side of a cube is x meters

So, the volume of a cube will be V=x3

Now the side x is increased by 2%, so the new length of side will be x(1+2100)=51x50

The new volume will be V1=(51x50)3=(5150)3x3

Therefore, the change in volume is V1V=((5150)31)x3

The percentage change in volume is :
=V1VV×100=⎜ ⎜ ⎜ ⎜5150311⎟ ⎟ ⎟ ⎟×100=(513503503)×100=7651125000×100=6.12%.

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