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 = πr2h:) What if the top costs twice as
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
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 - x2 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 = x3; 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) = 2x2 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 cm2 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 in3 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 = y2 and y = x.