The radius of a sphere shrinks from 10 to 9.8 cm. Find approximately the decrease in its volume.

Explanation

Volume of a sphere,
`V=4/3πr3`

`∴(dV)/(dr)=4/3π(3r^2)`

`⇒(dV)/(dr)=4πr^2`

Here,
`r=10cm`,`dr=9.8−10=−0.2cm`

`∴(dV)/(−0.2)=4π(10)^2`

`⇒dV=400πxx(−0.2)`
`=−80π`

So, decrease in volume of the sphere is `80πcm^3.`