How do you go about solving this problem below?

Question

At what rate, in stere per minute, is the volume of a sphere increasing if the radius of the sphere is two meters in length and is increasing at a rate of two meters per minute.


a. 32π

b. 48π

c. 72π

d. 108π

or is it none of these ?

Answer 1

What is a "stere"? Do you mean cubic meters per minute? Anyway, the volume of a sphere is (4/3) π r^3. So the rate of volume change is dV/dt = (4/3) π 3r^2 (dr/dt). The radius increases at 2m per minute, so dr/dt = 2. This means dV/dt simplifies to 8 π r^2. So the volume isn't increasing at a constant rate, but a rate that depends on what the volume is at the time. When r=2, the volume is increasing at a rate of 8 π 2^2 = 32π cubic meters per minute.

Answer 2

V = (4/3)pi*r^3
dV/dt = (4/3)*pi*3r^2 dv/dt= 4*pi*r^2 dv/dt
dV/dt = 4*pi*2^2*2 = 32pi meters cubed per minute

Answer 3

V = (4 /3).π.r ³
dV / dr = 4.π.r ²
dr / dt = 2
dV / dt = 4 π r ² x 2
dV / dt = 8 π r ²
dv / dt = 32π when r = 2
ANSWER a.

Answer 4

v= 4/3*pi*r^3

diff wrt to time.

dv/dt=4/3*pi*3r^2*dr/dt..

you know dr/dt and r ..

substitute to get the answer.dv/dt..

which is 32 pi.

Answer 5

V = (4/3)*π*r^3

dV/dt = 4π*r^2*(dr/dt)

dV/dt = 4π(4)(2)

dV/dt = 32π

Answer 6

Do your own homework, kid.

Answer 7

my answer is a