If the radius of a melting snowball decreases at a rate of 5 ins/min, find the rate at which the volume is decreasing when the snowball has diameter 4 inches

The rate at which the volume is decreasing when the snowball has a diameter of 4 inches is approximately 251.327 cubic inches per minute.

Step-by-step explanation:

Let suppose that snowball geometry correspond to a sphere. In this case, the volume of the sphere is:

(Eq. 1)

Where:

- Radius of the sphere, measured in inches.

- Volume of the sphere, measured in cubic inches.

We know that volume decreases due to melting, so we need an expression of the rate of change of volume in time. By differentiating (Eq. 1) we get:

(Eq. 2)

Where:

- Rate of change of the volume of the snowball in time, measured in cubic inches per minute.

- Rate of change of radius of the snowball in time, measured in inches per minute.

If we know that and , the rate at which the volume of the snowball is decreasing is:

The rate at which the volume is decreasing when the snowball has a diameter of 4 inches is approximately 251.327 cubic inches per minute.

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.