the radius of the right circular cylinder shown below is growing at a rate of 2ft/min while it's height is shrinking at 3ft/min. At what rate is the volume of the cylinder changing, with respect to time, when the radius is 4ft and the volume is 32 ft cubed.

The volume is decreasing at a rate of about 118.8 cubic feet per minute.

Step-by-step explanation:

Recall that the volume of a cylinder is given by:

Take the derivative of the equation with respect to t. V, r, and h are all functions of t:

Use the product rule and implicitly differentiate. Hence:

We want to find the rate at which the volume of the cylinder is changing when the radius if 4 feet and the volume is 32 cubic feet given that the radius is growing at a rate of 2ft/min and the height is shrinking at a rate of 3ft/min.

In other words, we want to find dV/dt when r = 4, V = 32, dr/dt = 2, and dh/dt = -3.

Since V = 32 and r = 4, solve for the height:

Substitute:

Therefore, the volume is decreasing at a rate of about 118.8 cubic feet per minute.

256π units²   (answer b)

step-by-step explanation:

the formula for the surface area of a sphere of radius r

is             a = 4πr²

and so, if r = 8 units, then the surface area is:

a = 4π(8 units)² = 256π units²   (answer b)

answer: just subtact the units and then add the non negative : happy to

step-by-step explanation: