Posted by **Mark** on Thursday, March 14, 2013 at 2:13pm.

A spherical balloon is being inflated in such a way that its radius increases at a rate of 3 cm/min. If the volume of the balloon is 0 at time 0, at what rate is the volume increasing after 5 minutes?

my answer is 45 cm/min.

is this right. thanks

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**Mark**, Thursday, March 14, 2013 at 2:50pm
Thank you!

- Word Problem-Calculus -
**Steve**, Thursday, March 14, 2013 at 3:23pm
way off.

First, volume is cm^3

v = 4/3 pi r^3

dv/dt = 4 pi r^2 dr/dt

at t=5, r=15 so

dv/dt = 4 pi * 225 * 3 = 2700 pi cm^3/min

How did you come up with 45? Way small, and I'd surely expect a pi to appear somewhere in any problem involving a sphere.

- Word Problem-Calculus -
**Mark**, Thursday, March 14, 2013 at 3:51pm
My fault lied in plugging in directly. Thank you for showing me the steps.

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