Practice with Applied Solids Topic Index | Geometry Index | Regents Exam Prep Center
 Answer the following questions dealing with solids.

Answers use = 3.141592654, the full calculator entry on the TI-83+/84+.

 1. Soda is sold in aluminum cans that measure 6 inches in height and 2 inches in diameter.  How many cubic inches of  soda are contained in a full can? (Round answer to the nearest tenth of a cubic inch.) Choose: 12.0 18.8 24.0 75.4 Explanation Use Volume formula for a cylinder. Volume=(pi)(radius squared)(height) V=(3.141592654)(1)(6) V=18.84955592

 2. A pharmacist is filling medicine capsules.  The capsules are cylinders with half spheres on each end.  If the length of the cylinder is 12 mm and the radius is 2 mm, how many cubic mm of medication can one capsule hold?  (Round answer to the nearest tenth of a cubic mm.) Choose:  32.7 150.7  184.3 202.6 Explanation Use the formula for volume of a cylinder and the formula for the volume of a sphere. The two half spheres together make up one complete sphere. Add the answers from each formula. Volume cylinder = 150.7964474 cubic mm Volume sphere = 33.51032164 cubic mm

 3. Pine bark mulch 6 inches deep is to be spread in each of the beds shown above.  Mulch is sold in bags containing one cubic yard.  How many bags of mulch will need to be purchased. Choose: 5 7 16 27 Explanation LOOK OUT!!! 6 inches = 0.5 feet. Volume of rectangular beds = lwh. Volume of circular bed = volume of cylinder =(pi) x (radius squared) x (height). One cubic yard = 27 cubic feet. Find total volumes and divide by 27. Volume rectangular beds = 25 + 25 + 50 = 100. Volume of circular bed = 88.35729338 Total volume = 188.3572934 Mulch = 6.976196051 bags = 7 bags.

 4. Ed works for an environmental protection agency which deals with land areas that have been contaminated by toxic waste.  The contaminated Choose: a. 1600.0  3920.4 7840.8 10890  b. 1600.0  3920.4 7840.8 10890  c. 160  392 393 784 soil covers an area of 1.62 acres.  Ed must remove the top 18 inches of soil in this area. 1 acre = 43,560 square feet 1 square yard = 9 square feet a.  What is the area of contaminated soil in square yards? Explanation (1.62 x 43,560) / 9 b.  What is the total volume of the contaminated soil in cubic yards? Explanation (7840.8) x (0.5) Remember 18 inches = .5 yards. c.  If each truck can haul 10 cubic yards of soil, how many full truckloads of contaminated soil will Ed be removing? Explanation 3920.4 / 10 Remember to round to the nearest truckload.

 5. The sphere appears in nature whenever a surface wants to be as small as possible.  Bubbles are an example of such a surface. If the diameter of a bubble is known to be 2 mm, what is the surface area of the bubble to the nearest square mm? Choose:  13 25  28 52 Explanation SA = 4 • pi • r² or pi • d²

 6. Choose:  2,095,533 20,955,334  43,442,812 74,350,037 The Pyramid of Khafre was built for the son of Khufa, for whom the Great Pyramid was built.  It is slightly smaller in size than the Great Pyramid. The height is 447.5 feet. The base side length is 706 feet. Find the volume of the Pyramid of Khafre to the nearest cubic foot. Explanation V = 1/3 • B • h Base is a square. B = s²

7.

"Happy" brand peanut butter is sold in differing size cylindrically shaped jars.  While buying a larger quantity of an item usually means a reduced unit price, purchasing larger jars of peanut butter does not always mean a savings.  Let's test Happy peanut butter to see which jar is the better buy.

 The large jar is 7 inches tall, has a diameter of 5 inches, and costs \$7.50. The smaller jar is 4.5 inches tall, has a diameter of 3 inches, and costs \$1.99.

Choose the best buy:

large jar
small jar

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