Spherical Balloon - Related Rates Problem

[rum2563]

[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.

 

[tiny-tim]

Hi rum2563!

Your answer looks right to me.

I think the book must have meant 200cm, not 2000.

 

[rum2563]

thanks very much. I thought so too. 2000 seems too much exaggerated. I am going to check with my teacher just to make sure. Thanks.