A spherical snowball is placed in the sun. The snowball melts so that it's surface area decreases at a rate of 2 cm2 /min. Find the rate at which the diameter decreases when the diameter is 8 cm

Question

A spherical snowball is placed in the sun. The snowball melts so that it's surface area decreases at a rate of 2 cm2 /min. Find the rate at which the diameter decreases when the diameter is 8 cm

Answer 1

surface area = π D² dA/dt = 2 π D dD/dt so dA/dt = 2 cm²/min = 2 π 8 dD/dt solving for dD/dt = 1/ 8 π cm/min

which gives .0398 cm/min