Question

At what approximate rate (in cubic meters per minute) is the volume of a sphere changing at the instant when the surface area is 3 square meters and the radius is changing at a rate of 1/5 meters per minute?

Answer 1

Answer: 3/5 cubic meters per minute

Explanation:

This is some epic algebra/calculus.

A = 4πr^2 = 3m^2

Volume:

V = 4/3 x πr^3

We want to change V with respect to t, with the knowledge that r with respect to t (dr/dt) is 1/5

Lets derive V

dV/dt = 4/3 x πr^2 x 3 x dr/dt

dV/dt = 4πr^2 x 1/5

BRUH MOMENT THOOOO

4πr^2 is a known value (the surface area from b4) :o, its 3!

dV/dt = 3/5

so the rate of change is 3/5 cubic meters per minute.