A conical tank (with vertex down) is 10 feet across the top and 12 feet deep.

Question

A conical tank (with vertex down) is 10 feet across the top and 12 feet deep. Water is flowing into the tank at a rate of 15 cubic feet per minute. Find the rate of change of the depth of the water when the water is 6 feet deep.

Answer 1

Step 1: Setup the formula for the volume of a cone.

V = (1/3)πr²h

Step 2: Use the radius and height of the cone to set up a proportion.

5/12 = r/6

r = 2.5

Step 3: Plug r = 2.5 into the volume equation.

V = 2.08πh

Step 4: Take the derivative with respect to t.

dV/dt = 2.08π(dh/dt)

Step 5: Plug in dV/dt = 15 and solve for dh/dt

15 = 2.08π(dh/dt)

dh/dt = 2.3