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January 27, 2015

January 27, 2015

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).

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