A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.4 cm/min. At what rate is the volume of the snowball decreasing when the radius is 13 cm.

Question

A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.4 cm/min. At what rate is the volume of the snowball decreasing when the radius is 13 cm. (Note the answer is a positive number).

Answer 1

Volume of ball is V = 4π/3r³; so dV/dt = 4π/3·3r²dr/dt = 4πr²dr/dt = 4π·13²cm²·0.4cm/min = 849.5 cm³/min