04/19/23 Perkins

AP Calculus AB

Day 11Section 2.6

1. The radius of a circle is increasing at a rate of 3 inches per second. Find the rate of change of the area of the circle when the radius is 3 feet.

Find .dA

dt

2A r

3 feetr

sec3 indr

dt

2dA dr

rdt dt

sec2 36 3 indA

indt

2

sec216 indA

dt

36 inches

21

3coneV r h

3

min10 ftdV

dt

2. Gravel is falling onto a conical pile at a rate of 10 cubic feet per minute. The diameter of the pile is five times the altitude. Find the rate of change of the height of the pile when the pile is 10 feet high.

Find .dh

dt

10 feeth

5d h2 5r h

5

2

hr

21 5

3 2

hh

325

12h

225

4

dV dhh

dt dt

22510 10

4

dh

dt

10 625dh

dt

min

2

125ft

dh

dt

Perkins

AP Calculus AB

Day 11Section 2.6

1. The radius of a circle is increasing at a rate of 3 inches per second. Find the rate of change of the area of the circle when the radius is 3 feet.

2. Gravel is falling onto a conical pile at a rate of 10 cubic feet per minute. The diameter of the pile is five times the altitude. Find the rate of change of the height of the pile when the pile is 10 feet high.