# math-calculus

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A spherical party balloon is being inflated with helium pumped in at a rate of 12 cubic feet per minute. How fast is the radius growing at the instant when the radius has reached 1 ft?

• math-calculus -

V = (4/3)πr^3
dV/dt = 4π r^2 dr/dt
given : dV/dt = 12 , and r = 1

12 = 4π (1) dr/dt
dr/dt = 3/π ft/min

• math-calculus -

Thank you! I initially thought the given rate of 12 cubic feet per minute was dr/dt.

• math-calculus -

The units are usually your give-away.

it says 12 cubic feet/min which is volume/time , so dV/dt

This will work in most cases.

• math-calculus -

12

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