Question

the radius of a sphere is increasing at a constant rate of 6 meters per second. at the instant when the radius of the sphere is 55 meters, what is the rate of change of the volume? the volume of a sphere can be found with the equation

Answer 1

228079.627 m^3/sec

Explanation:

First, establish the information you know.

- Given dr/dt = 6 m/sec

- When r = 55 m

- Find dV/dt

- the volume is by the formula V = 4/3 pi r^3 (the spaces are just automatically multiply)

Using the formula for the volume, take the derivative.

V = 4/3 pi r^3 --> dV/dt = 4 pi r^2 dr/dt (because you took the derivative)

Then plug all the information in and multiply. Don't forget the units.

dV/dt = 4 pi (55m)^2 (6 m/sec) = 228079.627 m^3/sec