Is vertical snowball is melting so that its diameter is decreasing at a rate of 0.4 cm/min. what is the rate that the volume of the snowballs changing one the diameter is 8 cm?

Question

Is vertical snowball is melting so that its diameter is decreasing at a rate of 0.4 cm/min. what is the rate that the volume of the snowballs changing one the diameter is 8 cm?

Answer 1

Hi,

snowball is sphere.

what does it mean? diameter is decreasing at a rate of 0.4 it means d = 2r------> d' = 2r'=-0.4----> r' = -0.2=dr/dt

you know volume of sphere is 4/3∏r³ and diameter = 8 it means r = 4

v = 4/3∏r³ -----> dv/dt = 4/3 ∏ 3 r² dr/dt-----> dv/dt =4 ∏ (4)² (-.02)= -12.8∏

I hope it is useful,

Minoo