Question

A spherical snowball is melting in such a way that it maintains its shape. The volume of the snowball is decreasing at a constant rate of cubic inches per minute. At the instant when the radius of the snowball is decreasing at a rate of inch per minute, what is the radius of the snowball, in inches?

Answer 1

The radius of the snowball at the instant when it is decreasing at a rate of 1 inch per minute is approximately 0.2827 inches. The formula for the rate of change of volume concerning time can be used to find the radius. By substituting the given values and solving for the radius, we find the approximate value. Thus the radius of the snowball at the instant when it is decreasing at a rate of 1 inch per minute is approximately 0.2827 inches.

Step-by-step explanation:

To find the radius of the snowball at the instant when it is decreasing at a rate of 1 inch per minute, we can use the formula for the rate of change of volume with respect to time:

V' = -4πr^2r'

Given that V' is -1 and r' is -1, we can substitute these values into the formula:

-1 = -4πr^2(-1)

Simplifying the equation, we have:

1 = 4πr^2

Dividing both sides by 4π, we get:

r^2 = 1/(4π)

Taking the square root of both sides, we find:

r = 1/(2√π)

Therefore, the radius of the snowball at the instant when it is decreasing at a rate of 1 inch per minute is approximately 0.2827 inches.