1. Write a formula for (a) the volume, (b) the total area, of a right prism whose altitude is h and whose base is a square of edge a. ( Ans: V = a2h, TA = 2a2+4ah ) 2. A lead pencil whose ends ends are hexagons was cut from a cylindrical cylindrical piece of wood, with the least waste. If the original piece was 8 in. long and ½ in. in diameter, find the volume of the pencil. ( Ans: 1.30 cu. in. ) 3. The base of a right triangular prism is a right triangle whose legs are 24 m. and 32 m. respectively. If the lateral edge is 14 m., what is the total area of the prism? ( Ans: 2,112 sq.m. ) 4. A masonry dam 40 ft. high has a uniform vertical cross section. The dam is 4 ft. wide at the top, 16 ft. wide at the bottom and is 80 ft. long. If its materials weigh 125 lbs. / cu. ft., find the weight of the dam. ( Ans: 4,000,000 lbs. ) 5. The lateral surface of a concrete octagonal pier of height 10 ft. is to be resurfaced. If each of the base edges is 1 ft., how many square feet of surfacing will be required? ( Ans: 80 sq. ft. ) 6. One part of a quartz crystal is a hexagonal prism with a right section of 1.29 sq. in., and an edge of 2.31 in., and a base of 1.41 sq. in. Find the altitude of the prism. ( Ans: 2.1134 in. ) 7. The lateral area of a prism is 448 sq. m. If the lateral edge is 7 m., what is the perimeter of the right section? ( Ans: 64 m. ) 8. Find the volume of the right triangular prism whose altitude is 15 cm. and whose base is an equilateral triangle with side 6 cm. long. ( Ans: 234 cu.cm.) 9. In the figure shown, the trough has trapezoidal ends which lie in parallel palnes. The top of the trough is a horizontal rectangle 6 ft. by 16 ft. and the depth of the trough is 4 feet. a. How many cubic feet of water can it hold? b. How many cubic feet of wate r does it contain when the depth o f the water is 3 ft.? c. What is the area covered by water (wet portion of the container) with this height? 6’
16’
4’
x 4’
(Ans: a. 320 cu. ft.
b. 228 sq. ft.
c. 191.38 sq. ft.)
10. A piece of slab with two parallel equal bases each in the form of a sector weighs 10 grams per cubic inch. Find its total mass in kilograms.
35°48’
15’
8’
(Ans: 3 kg) 11. The average depth of a lake is estimated to be 40 ft. If the surface area is 15 acres, find the volume of water in the lake. ( one acre = 43,560 sq. ft.) (Ans: 26,136,000 cu. ft. ) 12. An indoor roller-skating rink with an area of 1,500 sq. yard has a concrete flooring 3 in. thick. Find the amount of concrete used in laying the floor. ( Ans: 125 cu. yard ) 13. A paint manufacturer desires a cylindrical steel drum to hold 50 gal. of roof paint. For convenience in handling, it is found necessary to limit the inside diameter to 2 ½ ft. Find the height of the drum desired. ( One gallon = 231 cu. in.) ( Ans: 1.36 ft. ) 14. Find the waste in making the largest possible cylindrical rod from a bar of iron 3 ft . long which has a square cross section whose diagonal is 6 in. ( Ans: 139 cu.in. ) 15. A cubic foot of water weighs about 62.4 lbs. What must be the diameter of a cylindrical pail 1 ft. high in or der for it to hold the water from 25 lbs of ice? How many square inches of sheet tin are required to make the pail? ( Ans: 8.57 in; 380.79 sq. in ) 16. If a lead pipe ¼ in. thick has an inner diameter of 1 ½ in., find the number of cubic inches of lead in a piece of pipe 10 ft. long. ( Ans: 164.94 cu. in. ) 17. The diameter of a well is 6 ft., and the water is 7 ft. deep. How many gallons of water are there in the well, reckoning 7.48 gallons to a cubic foot? ( Ans: 1480.4 gal. )
18. A cylindrical standpipe is to contain 343,000 g allons of water. If its height is to be twice its diameter, what must be the dimensions?
( Ans: 30.79 ft. by 61.58 ft. ) 19. When a body is immersed in water in a right circular cylinder 60 cm. in diameter, the level of the water rises 40 cm. What is the volume of the body? (Ans: 113,100 cu.cm. ) 20. The covered water reservoir in a certain town is 18 m. high with a base diameter of 6 m. Find the volume of water it contains when full in liters. (Ans: 508,938 Liters) 21. The exterior of the reservoir in the previous problem, including the top is to be painted with two coats of paints. Assuming that one liter of paint will cover 20 sq. m., how many liters are required? ( Ans: 36.80 L) 22. A rectangle, 3 cm. wide and 8 cm. long, is being revolved about its longer side. Find the total ar ea and the volume of the cylinder generated. (Ans: 66π sq.cm. / 72π cu. cm.) 23. Determine the radius of a right circular cylinder if it has a lateral area of 88 sq. cm. and has a volume of 220 cu. cm. ( Ans: 5 cm. ) 24. A metal washer 1 in. in diameter is pierced by ½ in. hole. What is the volume of the washer if it is 1/8 in. thick? (Ans: 0.074 cu. in.)
