Question

the radius of a sphere is increasing at a rate of 3 mm/s. how fast is the volume increasing (in mm3/s) when the diameter is 100 mm? (round your answer to two decimal places.)

Answer 1

94,247.78 mm^3/s to 2 D.P,'s.

Explanation:

The formula for the volume in terms of the radius is:

V = 4/3 π r^3

Differentiating with respect to r:

dV/dr = 4/3 * 3* π r^2

= 4 π r^2

Rate of change of V with respect to time

= dV/dt

Rate of change of radius = dr/dt = 3

When radius ( = 1/2 diameter) = 50

dV/dt = dV/dr * dr/dt

= 4 π (50)^2 * 3

= 94247.77961.