related rates help please!!

Question

A spherical balloon is being inflated so that its volume is increasing at the rate of 10cm3/sec. Find the rate at which the diameter is increasing when the diameter is 20cm?

 

Answer 1

V = (4/3)·pi·r³

• V = volume of balloon
• r = radius of balloon

 

dV/dt = dV/dr · dr/dt      [Chain Rule]

dV/dt = 4·pi·r² · dr/dt        

 

Plug in dV/dt = 10 cm³/sec and r = 20 cm and solve for dr/dt.

That will give the rate at which the radius is changing. The diameter is changing at twice the rate.