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**[SOLVED] Spherical Balloon - Related Rates Problem**

## Homework Statement

A spherical balloon is inflated so that its radius increases at a rate of 1 cm/min. How fast is the volume increasing when:

a) the diameter is 2000 cm

b) the surface area is 324 pi cm^2 ---> I have solved this already

## Homework Equations

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

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

## The Attempt at a Solution

For part (a) the diameter is 2000 cm.

So I make it 1000 cm for Radius

Now, I put it in the equation:

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

where dr/dt = 1cm/min

dV/dt = 4pi(1000^2)(1 cm/min)

= 4 000 000 pi cm^3 / min

But, the answer in the book is 40 000 pi cm^3 / min.

Please help me out. Thanks.