# Calculus I: Sample Exam 4

1. A right circular cylinder is to be designed to hold 22 cubic inches of

coca-cola (approximately 12 fluid ounces). To keep the costs down, we

want to use a minimum of material in the construction. (The volume

of a cylinder is given by V = πr^{2}h:) What if the top costs twice as

much.

2. A rectangular open tank is to have a square base, and its volume is to

be 125 cubic yards. The cost per square yard for the base is $8 and for

the sides is $4. Find the dimensions of the tank in order to minimize

the cost.

3. A box with an open top is to be constructed from a 15" by 24" piece of

cardboard by removing equal size squares from each corner and folding

the resulting flaps upward. The box with the largest volume will have

a height of

4. Solve by horizontal strips only. The area bounded by the curves y =

2 - x^{2} and x + y = 0

5. The area bounded by the lines y = x, x + 2y = 6 and the x axis is:

6. The volume of the solid generated by revolving about the x-axis the

region bounded by the graphs of y = x^{3}; x = 2, and the x-axis.

7. What is the volume of revolution from x = 0 to x = 3/2 when the

function f(x) = 2x^{2} is revolved around the y - axis.

8. The radius of a circle is decreasing at a rate of 0:5 cm per second. At

what rate, in cm^{2} per second, is the circle's area decreasing when the

radius is 4 c

9. A spherical ball of ice with an initial radius of 4 inches melts at a rate

of 2 in^{3} per minute. How fast is the radius of the ball decreasing when

the radius is 3 inches?

10. The volume of the solid generated by revolving about the x-axis the

region bounded by the graphs of
x = 0, and y = 2.

11. The volume of the solid generated by revolving about the x-axis the

region bounded by the graphs of x = y^{2} and y = x.