Page 334 - Calculus Demystified

Final Exam
square foot, and the circular top and bottom of material costing $2 321
per square foot. What dimensions will result in the most economical
tank?
√ √
(a) height = 4 · 3 π/25, radius = 3 π/25
√ √
(b) height = 3 25/π, radius = 4 · 3 25/π
(c) height = 5 1/3 , radius = π 1/3
(d) height = 4, radius = 1
√ √
(e) height = 4 · 3 25/π, radius = 3 25/π
39. A pigpen is to be made in the shape of a rectangle. It is to hold 100 square
feet. The fence for the north and south sides costs $8 per running foot, and
the fence for the east and west sides costs $10 per running foot. What shape
will result in the most economical pen?
√ √
(a) north/south = 4 5, east/west = 5 5
√ √
(b) north/south = 5 5, east/west = 4 5
√ √
(c) north/south = 4 4, east/west = 5 4
√ √
(d) north/south = 5 4, east/west = 4 4
√ √
(e) north/south = 5, east/west = 4
40. A spherical balloon is losing air at the rate of 2 cubic inches per
minute. When the radius is 12 inches, at what rate is the radius
changing?
(a) 1/[288π] in./min
(b) −1 in./min
(c) −2 in./min
(d) −1/[144π] in./min
(e) −1/[288π] in./min
41. Under heat, a rectangular plate is changing shape. The length is
increasing by 0.5 inches per minute and the width is decreasing by
1.5 inches per minute. How is the area changing when = 10 and
w = 5?
(a) The area is decreasing by 9.5 inches per minute.
(b) The area is increasing by 13.5 inches per minute.
(c) The area is decreasing by 10.5 inches per minute.
(d) The area is increasing by 8.5 inches per minute.
(e) The area is decreasing by 12.5 inches per minute.