Calc Area Review

• C
• A
• E
• B

• Intermediate Value Theorem
• Rolle's Theorem
• Average Rate of Change
• Average Value of f

The radius of a sphere is decreasing at a rate of 2 cm/sec.  At the instant when the radius of the sphere is 3 cm, what is the rate of change, in cm²/sec, of the surface area of the sphere?  (The surface area of a sphere is A = 4πr².)

• -108π

• -72π

• -48π

• -24π

We need to enclose a field with a fence. We have 500 feet of fencing material and a building is on one side of the field so we won't need any fencing on that side. Determine the dimensions of the field that will enclose the largest area.

• x=250 ft, y=125 ft

• x=150 ft, y=200 ft

• x=125 ft, y=100 ft

• x=200 ft, y=150 ft

Disk/Washer Method

• B

• C

• D

• E

The radius of a circle is increasing at a constant rate of 0.2 meters per second.  What is the rate of increase in the area of the circle at the instant when the circumference of the circle is 20π meters?

• 0.04π m²/sec

• 0.4π m²/sec

• 4π m²/sec

• 20π m²/sec

• A

• B

• C

• D

• E

(Calc OK): Find the area inside the inner loop r = 1 + 2 cosθ.

• 0.544

• 1.087

• 8.338

• 8.881

• 9.424

Find the area outside the curve r = 3cosθ and inside r = 1 + cosθ.

• 0.204

• 0.393

• 0.596

• 0.785

• 1.570

(Calc OK) Find the area enclosed inside the 8-petaled rose r = 8cos(4θ).

• 12.567

• 25.133

• 50.265

• 110.531