# [SOLVED] Speed of increase

• Mar 1st 2010, 12:16 PM
Revy
[SOLVED] Rate of increase
Could someone help me with this one?

Sphere radius is increasing in the course of time. At the time moment when it's radius is 8cm, it's increasing in 5cm/s speed. At what speed does spheres volume increase?
• Mar 1st 2010, 12:52 PM
Quote:

Originally Posted by Revy
Could someone help me with this one?

Sphere radius is increasing in the course of time. At the time moment when it's radius is 8cm, it's increasing in 5cm/s speed. At what speed does spheres volume increase?

$\displaystyle \frac{dV}{dt}=\frac{d}{dt}\left(\frac{4}{3}{\pi}r^ 3\right)=\frac{4}{3}{\pi}\frac{d}{dt}r^3=\frac{4}{ 3}{\pi}\frac{dr}{dt}\frac{d}{dr}r^3$

When r=8, $\displaystyle \frac{dr}{dt}=5\ cm/s$

From this, the rate of increase in volume can be calculated.
• Mar 1st 2010, 01:04 PM
HallsofIvy
This is a "relative rates" problem and belongs in "Calculus", not "differential equations".
• Mar 1st 2010, 01:23 PM
Revy
hm.. is that the same?
$\displaystyle V' = \frac {4}{3}{\pi} {3r^2} {r'} = \frac {4}{3}{\pi}* {3*8^2*5}= 1280{\pi}$

Quote:

Originally Posted by HallsofIvy
This is a "relative rates" problem and belongs in "Calculus", not "differential equations".

Sorry, at first I wasn't sure where I should post it. It's my first time facing english mathematical terms