The volume of a sphere is decreasing at a constant rate of 20πcm^3/s..?

Science & Mathematics by Anonymous 2018-07-11 14:05:28

Social Science

3 answers

find the radius in cm of the sphere at the instant when the radius is decreasing at a rate of 0.2cm/s [Volume of sphere, V = 4/3 πr^3]

Anonymous

Ans. r=5 cm.
Anonymous

dV/dt = 4πr^2 dr/dt; dV/dt = 20πcm^3/s and dr/dt = 0.2 cm/s so {[dV/dt]/[4π(dr/dt)]}^0.5 = r
Anonymous

dV/dt = -20π cm³/sec = 4πr²dr/dt dr/dt = -5/r² = -0.2 cm/sec r² = 25 cm² r = 5 cm