The rate of growth of the volume of a sphere is proportional to its volume

MATHEMATICS · Subjective · AP · Calculus AB · Differential Equations · Differential Equations

Problem

6. The rate of growth of the volume of a sphere is proportional to its volume. If the volume of the sphere is initially

36 \pi \mathrm{ft}^{3}

, and expands to

90 \pi \mathrm{ft}^{3}

after 1 second, find the volume of the sphere after 3 seconds.