Question

if volume of a sphere is increasing at rate of 24 cubic inche per minute and surface area increaing 12 inches per minute what is radius

Answer 1

r= 4 in

Step-by-step explanation:

Given that

`(dV)/(dt)=24\ in^3/min`

`(dA)/(dt)=12\ in^2/min`

The volume of the sphere

`V=(4)/(3)\pi r^3`

`(dV)/(dt)=4\pi r^2(dr)/(dt)` ------------1

The surface area

A=4 πr²

`(dA)/(dt)=8\pi r(dr)/(dt)`

`(dA)/(dt)=2* 4\pi r(dr)/(dt)` -----2

Form equation 1 and 2

`(dV)/(dt)=r* ((dA)/(dt))/(2)`

24 x 2 = r x 12

r= 4 in