Sample Problems Prism Cylinder

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<ul><li><p>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 </p><p>edge a. </p><p>( Ans: V = a2h, TA = 2a2+4ah ) </p><p>2. A lead pencil whose ends are hexagons was cut from a cylindrical piece of wood, with the least waste. If the original </p><p>piece was 8 in. long and in. in diameter, find the volume of the pencil. </p><p> ( Ans: 1.30 cu. in. ) </p><p>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 </p><p>14 m., what is the total area of the prism? </p><p>( Ans: 2,112 sq.m. ) </p><p>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 </p><p>and is 80 ft. long. If its materials weigh 125 lbs. / cu. ft., find the weight of the dam. </p><p>( Ans: 4,000,000 lbs. ) </p><p>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 </p><p>many square feet of surfacing will be required? </p><p>( Ans: 80 sq. ft. ) </p><p>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 </p><p>of 1.41 sq. in. Find the altitude of the prism. </p><p>( Ans: 2.1134 in. ) </p><p>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? </p><p>( Ans: 64 m. ) </p><p>8. Find the volume of the right triangular prism whose altitude is 15 cm. and whose base is an equilateral triangle with </p><p>side 6 cm. long. </p><p>( Ans: 234 </p><p>9. In the figure shown, the trough has trapezoidal ends which lie in parallel palnes. The top of the trough is a horizontal </p><p>rectangle 6 ft. by 16 ft. and the depth of the trough is 4 feet. </p><p>a. How many cubic feet of water can it hold? </p><p>b. How many cubic feet of water does it contain when the depth of the water is 3 ft.? </p><p>c. What is the area covered by water (wet portion of the container) with this height? </p><p>16 </p><p>6 </p><p>4 </p><p>4 </p><p>x </p></li><li><p>(Ans: a. 320 cu. ft. b. 228 sq. ft. c. 191.38 sq. ft.) </p><p>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 </p><p>mass in kilograms. </p><p>(Ans: 3 kg) </p><p>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 </p><p>lake. ( one acre = 43,560 sq. ft.) </p><p>(Ans: 26,136,000 cu. ft. ) </p><p>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 </p><p>concrete used in laying the floor. </p><p> ( Ans: 125 cu. yard ) </p><p>13. A paint manufacturer desires a cylindrical steel drum to hold 50 gal. of roof paint. For convenience in handling, it is </p><p>found necessary to limit the inside diameter to 2 ft. Find the height of the drum desired. ( One gallon = 231 cu. in.) </p><p>( Ans: 1.36 ft. ) </p><p>14. Find the waste in making the largest possible cylindrical rod from a bar of iron 3 ft. long which has a square cross </p><p>section whose diagonal is 6 in. </p><p>( Ans: 139 ) </p><p>15. A cubic foot of water weighs about 62.4 lbs. What must be the diameter of a cylindrical pail 1 ft. high in order for it </p><p>to hold the water from 25 lbs of ice? How many square inches of sheet tin are required to make the pail? </p><p>( Ans: 8.57 in; 380.79 sq. in ) </p><p>16. If a lead pipe in. thick has an inner diameter of 1 in., find the number of cubic inches of lead in a piece of pipe 10 </p><p>ft. long. </p><p>( Ans: 164.94 cu. in. ) </p><p>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, </p><p>reckoning 7.48 gallons to a cubic foot? </p><p>( Ans: 1480.4 gal. ) </p><p>18. A cylindrical standpipe is to contain 343,000 gallons of water. If its height is to be twice its diameter, what must be </p><p>the dimensions? </p><p>15 </p><p>8 </p><p>3548 </p></li><li><p>( Ans: 30.79 ft. by 61.58 ft. ) </p><p>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. </p><p>What is the volume of the body? </p><p>(Ans: 113,100 ) </p><p>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 </p><p>contains when full in liters. </p><p>(Ans: 508,938 Liters) </p><p>21. The exterior of the reservoir in the previous problem, including the top is to be painted with two coats of paints. </p><p>Assuming that one liter of paint will cover 20 sq. m., how many liters are required? </p><p>( Ans: 36.80 L) </p><p>22. A rectangle, 3 cm. wide and 8 cm. long, is being revolved about its longer side. Find the total area and the volume of </p><p>the cylinder generated. </p><p>(Ans: 66 / 72 cu. cm.) </p><p>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. </p><p>( Ans: 5 cm. ) </p><p>24. A metal washer 1 in. in diameter is pierced by in. hole. What is the volume of the washer if it is 1/8 in. thick? </p><p>(Ans: 0.074 cu. in.) </p></li></ul>