Hello, Sky12!

This problem doesn't involve the Chain Rule.

Exactlywhereis your difficulty?

The amount of fluid in a partially-filled spherical tank

. . is given by: .

where is the radius of the tank, and is the depth at the center of the tank.

If fluid is pumped into the tank at a rate of 8 m³/min, and m,

how fast is the fluid rising when the tank is 3/4 full?

We have: .

Differentiate with respect to time: .

Then: .

. . We are given m³/min . . . When the tank is full: m.**

Therefore: . m/min

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

**. No, I didn't make an error . . .

If the tank is three-fourth full, then: .

. . and we have a cubic equation to solve: .

which has a root near