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

Answer:

r= 4 in

Explanation:

Given that

$\dfrac{dV}{dt}=24\ in^3/min$

$\dfrac{dA}{dt}=12\ in^2/min$

The volume of the sphere

$V=\dfrac{4}{3}\pi r^3$

$\dfrac{dV}{dt}=4\pi r^2\dfrac{dr}{dt}$           ------------1

The surface area

A=4 πr²

$\dfrac{dA}{dt}=8\pi r\dfrac{dr}{dt}$    

$\dfrac{dA}{dt}=2\times 4\pi r\dfrac{dr}{dt}$               -----2

Form equation 1 and 2

$\dfrac{dV}{dt}=r\times \dfrac{\dfrac{dA}{dt}}{2}$

24 x 2 = r x 12

r= 4 in