Question

The radius of a sphere is increasing at a rate of 4mm/s. How fast is the volume increasing when the diameter is 80 mm?

Answer 1

"Radius of a sphere is increasing at a rate..."
dr/dt = 4
"How fast is volume increasing?"
We need to find dV/dt

drdt∗dVdr=dVdt
So we have a way to find it, but we must first find dV/dr. How do we find dV/dr?
V=(4/3)pi*r^3
Derive with respect to r.

Answer 2

metal please

Answer 3

make diamerter a radius

Answer 4

so what happens to the 80mm? do we not include that in the formula?

Answer 5

include it

Answer 6

so

Answer 7

i will put in formula

Answer 8

This is what I had previously dV/dr = 4pi squared*80*4

Answer 9

First off you are looking for dv/dt.

Therefore set up an equation like this: dv/dt = dv/dr * dr/dt

We know that dr/dt = 4 mm/s

The formula of volume for a sphere is (4/3)pi * r^3.

The diameter is 80mm, therefore the radius is 40 mm.

When you differentiate the volume equation, you will get 4pi*r^2.

Now plug in 40 for the radius into the volume equation and multiply that by 4 mm/s.

It will look like dv/dt = 4pi(40)^2 * 4 mm/s

That will give you the rate at which the volume is increasing when the diameter is 80 mm.

Hope this helps.

Answer 10

metal please

Answer 11

43.14*radius to 2nd power

Answer 12

*4 times 3.14 times radius to 2nd power

Answer 13

dicided by 3

Answer 14

medal please