Question

a spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.2 cm/min. at what rate is the volume of the snowball decreasing when the radius is 10 cm. (note the answer is a positive number).

\\(\text{cm}^3/\text{min}\\)

Explanation:

Relate volume and radius of a sphere

$$ V = \frac{4}{3}\pi r^3 $$

Differentiate with respect to time

$$ \frac{dV}{dt} = 4\pi r^2 \frac{dr}{dt} $$

Substitute given values and solve

$$
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Answer:

A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.2 cm/min. At what rate is the volume of the snowball decreasing when the radius is 10 cm. (Note the answer is a positive number).

<blank>\(80\pi\)</blank> \(\frac{\text{cm}^3}{\text{min}}\)