Practice with Volume and Surface Area Topic Index | Algebra 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. Be sure to use the radius of 1 in. Volume=(pi)(radius squared)(height) V=(pi)(1 squared)(6) V=18.84955592

 2. Pine bark mulch 6 inches deep is to be spread in each of the beds shown above.  Mulch is sold by the cubic yard.  To the nearest cubic yard, how much 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.

3.
 Ed works for an environmental protection agency which deals with land areas that have been contaminated by toxic waste.  The contaminated 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?

Choose:
a.

1600.0
3920.4
7840.8
10890

b.
1600.0
3920.4
7840.8
10890

c.
160
392
393
784

b.  What is the total volume of the contaminated soil in cubic yards?

c.  If each truck can haul 10 cubic yards of soil, how many full truckloads of contaminated soil will Ed be removing?

 4. A company manufactures large dice for children's games.  The dice are cubes with one side measuring 1.2 inch in length.  The dice are formed when a liquid plastic in is poured into a mold of the die.  The company uses trays that contain one dozen die molds in each tray.  If the liquid plastic is measured in cubic inches, how much liquid plastic is needed to fill one tray?  (Round answer to the nearest tenth of a cubic inch) Choose:  14.4 17.3 20.7 172.8 Explanation The formula is V = l x w x h where l = w = h for a cube. So V = l x l x l. The volume is 1.2 x 1.2 x 1.2 = 1.728. There are 12 die in each tray. 1.728 x 12 = 20.736. Round to nearest tenth: 20.7

 5. Extra Challenging 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

 6. a.  Find the volume, to the nearest tenth of a cubic foot, of this container              b.  Find the surface area, to the nearest tenth of a square foot, of this container assuming it has a closed top and bottom. Choose: a.  4712.4 2650.7  1767.1 1178.1  b.  132.7 471.2  628.3 1178.1 Explanation Be sure you are using a radius of 5. Since the top and bottom are included in surface area, use the complete formula.

 7. Find the surface area of this container assuming it has an open top.  The bottom is closed. (Round answer to the nearest tenth of a sq. cm.) Choose:  301.6 351.9  251.3 421.6 Explanation Since only the top is missing, the formula will be SA = 2(pi)rh + (pi)rē Only ONE area of circle section is used.

 8. A box needs to be covered in brown paper for mailing.  If the box measures 3 feet by 3 feet by 2 feet, what is the surface area of the box that will need to be covered?  The box is closed. Choose:  18 sq. ft. 42 sq. ft.  48 sq. ft. 54 sq, ft. Explanation Find the area of each surface. Add the areas together.

9.

When buying a room air conditioner, it is important to purchase a unit that is neither too big nor too small for the room.  If the unit is too large, it will cool too quickly and will not remove humidity from the air, thus wasting money and energy.  If the unit is too small, it will run continually without ever cooling to the desired temperature, again wasting energy and money.

a.)  Find the total cubic feet of living space for the bedroom below. The ceiling is 7 feet high.

b.)  Which of these 3 air conditioning models would be the best purchase for this bedroom?
Model A:  for rooms 900 to 1100 cubic feet
Model B:  for rooms 1100 to 1300 cubic feet
Model C:  for rooms 1300 to 1500 cubic feet

Choose:
a.

924
1124

1176
1476

b.

A
B
C

 10. A box is to be wrapped in a shiny red decorative paper.  The box is 9 inches long, 5 inches wide, and 4 inches high. Choose: a) 112 sq. in. 180 sq. in.  202 sq. in. 260 sq, in. a.)  What is the minimum amount of decorative paper needed to        cover the box? b.)  If the box contains confetti, how many cubic inches of       confetti are needed to fill the box? Choose: b) 112 cu. in. 180 cu. in.  202 cu. in. 260 cu. in. Explanation a.) Find the area of each surface. SA = 2lw + 2lh + 2wh b.) V = l w h

 11. A cylindrical container has a diameter of 12 inches and a height of 15 inches, as illustrated in the diagram.  What is the volume of this container to the nearest tenth of a cubic inch? Choose: 6,785.8 4,241.2 2,160.0 1,696.5 Explanation Use Volume formula for a cylinder. Volume=(pi)(radius squared)(height) Be sure to use a radius of 6 inches. V=(pi)(6 squared)(15) V=1696.46003294

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