The radius of a spherical watermelon is growing at a constant rate of 2 centimeters per week. The thickness of the rind is always one tenth of the radius.

Question

 The radius of a spherical watermelon is growing at a constant rate of 2 centimeters per week. The thickness of the rind is always one tenth of the radius. The volume of the rind is growing at the rate  cubic centimeters per week at the end of the fifth week. Assume that the radius is initially zero.

Answer 1

v = 4π/3·(1.1r)³ (we consider external volume); dv/dt = 4π·(1.1)³·r²·dr/dt = 4π(1.1)³·10²·2 = 3345.17 cm³/week

r = 2cm/week·5week = 10 cm