Question

the radical of a psherical ball is decreasing at a constant rate of 3cm per second. find in cubic centimeters per second

Answer 1

Volume will decrease at a rate of
`12\pi r^2m^3/sec`

Explanation:

We have given rate of change of radius is 3 cm per second

So
`(dr)/(dt)=3cm/sec`

Volume of the ball is given as
`V=(4)/(3)\pi r^3`

So
`(dV)/(dt)=4\pi r^2(dr)/(dt)`

As
`(dr)/(dt)=3cm/sec`

So
`(dv)/(dt)=4\pi r^2* 3=12\pi r^2m^3/sec`

So volume will decrease at a rate of
`12\pi r^2m^3/sec`