On being heated, the length of each side of a cube increases by 2%. What is the percentage increase in the volume of the cube?

Explanation

If l is the length of the cube of volume V, then
`" "V=l^(3)" …(1)"`
`therefore " "dV=3l^(2)dl" ...(2)"`
or, `" "(dV)/V=(3l^(2)dl)/l^(3)=(3dl)/l. " Given, " (dl)/l=2/100.`
`therefore " "(dV)/V=3/l*(2l)/100=6/100`
`therefore` Increase in volume `=6/100 times 100%=6%.`