Question

A spherical snowball is melting in such a way that its volume is decreasing at a rate of 2 cm/min. At what rate is the radius changing when the radius is 7 cm? [The volume of a sphere is given by V = (4/3)πr³.]

A) -1/72 cm/min
B) -1/4977 cm/min
C) -1/9870 cm/min
D) -1/1967 cm/min

Answer 1

The rate at which the radius is changing when the radius is 7 cm is -1/72 cm/min.

Step-by-step explanation:

To find the rate at which the radius of the snowball is changing when the radius is 7 cm, we need to use the rate of change of the volume with respect to time.

The volume of a sphere is given by the formula V = (4/3)πr³. Differentiating both sides of the equation with respect to time gives us dV/dt = 4πr²(dr/dt).

We know that dV/dt = -2 cm³/min (since the volume is decreasing) and r = 7 cm. Plugging these values into the equation and solving for dr/dt, we get dr/dt = -1/72 cm/min.

Therefore, the rate at which the radius is changing when the radius is 7 cm is -1/72 cm/min.