Tuesday

July 22, 2014

July 22, 2014

Posted by **james** on Thursday, December 30, 2010 at 3:25pm.

- related rates problem-calculus -
**Marth**, Thursday, December 30, 2010 at 3:36pmThe balloon is spherical, so

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

SA = 4(pi)r^2

Differentiate both with respect to time.

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

dSA/dt = 8(pi)r(dr/dt)

We're given the rate of change in SA and need to find the rate of change in volume. Let's write an equation for it.

(dV/dt)/r = 4(pi)r(dr/dt)

(dSA/dt)/2 = 4(pi)r(dr/dt)

(dV/dt)/r = (dSA/dt)/2

(dV/dt) = (r/2)(dSA/dt)

- related rates problem-calculus -
**Marth**, Thursday, December 30, 2010 at 3:38pmEdit: actually we're given dr/dt and SA.

Since dV/dt = 4(pi)r^2(dr/dt) and SA = 4(pi)r^2, dV/dt = SA(dr/dt).

**Related Questions**

AP calculus AB - A spherical balloon is being filled with air in such a way that...

help on calculus - A spherical balloon is being filled with air in such a way ...

calculus - Air is being pumped into a spherical balloon so that its volume ...

Calculus - Air is being pumped into a spherical balloon so that its volume ...

math - Air is pumped into a balloon such that its volume increases at the rate ...

related rates calculus problem - A balloon is being filled with air at a rate of...

Calculus - a spherical balloon is inflated with gas at the rate of 500 cubic ...

Calculus - Air is being pumped into a spherical balloon and the volume is ...

Word Problem-Calculus - A spherical balloon is being inflated in such a way that...

relaited rates - A spherical balloon is being inflated so that its volume is ...