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Rate at which the volume of a spherical balloon is decreasing?
A spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.4 cm/min. At what rate is the volume** of the snowball decreasing when the diameter is 9 cm? (Note the answer is a positive number)
Please show work along with the answer.
1 Answer
- Spaceman SpiffLv 71 decade agoFavorite Answer
We are given the rate of change of the diameter is 0.4 cm/min, or a change of radius, dr/dt = 0.2 cm/min.
The volume of a sphere is given by:
V = (4/3)πr³
The rate of change of the volume, dV/dt, is given by:
dV/dt = 4πr²(dr/dt) = 4π(9)²(0.2) = (324/5)π = 203.575 cm³/min
