11/5- Warmup Pop Quiz

Ethan is sitting on the edge of a dock tossing rocks into the water. As each rock hits the water, small circles appear traveling outward from the point of impact. The radius of the circle is changing at a rate of 5 in/sec. How fast is the area of the outer circle changing when the diameter is 8 in?

• 80pi in/sec

• 20pi in/sec

• 60pi in/sec

• 4opi in/sec

A water tank, shaped like an inverted circular cone, has a base radius of 6 ft and a height of 9 ft. The tank is completely full and needs to be drained. **The valve is opened and the water begins to decrease at a rate of 2 ft³/sec.**  Which of these expressions represents the ** information?

• none of these

• 35

• 40.625

• 32.1

• 41

A Riemann Sum uses rectangles to

• approximate the area under a curve. The more rectangles, the better the approximation.

• approximate the area under a curve. The less rectangles, the better the approximation.

• approximate the area under a curve. The more rectangles, the worse the approximation.

Use a right Riemann Sum to approximate the area of the shaded area.

• 12

• 9

• 10

• 5

What is the approximate area of the region, using 4 subintervals and heights using left values?

• 7.5

• 7.75

• 10

• 11.5