Question 1:

Determine the volume of a sphere of radius r. (A sphere is swept out when the region bounded by the x-axis and the top half of the circle x2 + y2 = r2 is revolved about the x-axis.)

Question 2:

Calculate the length of for 1 ≤ x ≤ 9.

Question 3:

Find the area of the surface when the graph of is rotated about the x-axis

(a) for 0 ≤ x ≤ 1
(b) for 1 ≤ x ≤ 2
(c) for 2 ≤ x ≤ 3

Question 4:

How much work is done pushing the box in the figure below:

(a) from x = 3 to x = 7 feet?
(b) from x = 0 to x = 7 feet?

Question 5:

The empty can in the figure below weighs 1 ounce when empty and 13 ounces when full. Write the height of the center of mass of the can-liquid system as a function of the height of the liquid in the can.