Questions

1) The shape of the truck’s trailer is a rectangular prism with a base that measures 15 feet by 6 feet. The height of the truck trailer is 4 feet. What is the volume of the trailer?

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2) A driveway has the following dimensions: length of 75 feet, width of 20 feet, and thickness of 8 INCHES. (a) What is the volume of the driveway in CUBIC FEET? (Hint: Change all units to feet before solving.) (b) How much concrete (in cubic yards) is needed to pave the driveway? Round up to the nearest cubic yard so that there will be enough cement to complete the driveway.

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3) The measurements of the box shown below are 6 inches by 4 inches by 5 inches. (a) How many unit cubes (1 inch by 1 inch by 1 inch) cover the base of the box? (b) How many unit cubes can be packed in the box? (c) What is the volume of the box?

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4) What is the volume of the trapezoidal prism shown below?

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5) What is the volume of the right prism shown below?

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6) An architect designs an A-frame house with the floor measuring 35 feet by 56 feet. The front of the house has the shape of an equilateral triangle with all sides measuring 35 feet. Answer the following questions: (a) What is the height of the triangular front of the house? (Hint: Recall that the height of an equilateral triangle divides the triangle into two 30-60-90-degree right triangles.) (b) What is the area of the triangular front of the house? (c) What is the volume of the house?

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7) Which of the numbers below is NOT a perfect cube (a number that is an integer multiplied by itself three times)? Use a scientific calculator to help determine the answer.

a.) 1,331

b.) 1,728

c.) 2,744

d.) 3,724

8) Use approximation to find the cube root of 450 rounded to the nearest hundredth, and then answer the following questions: (a) The number, 450, falls between what two perfect cubes? (b) What are the cube roots of these two perfect cubes? (c) Between what two decimal numbers, expressed in tenths, does the cube root of 450 fall? (d) To the nearest hundredth, the cube root of 450 is closest to what number?

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9) The cube root of 625 will need to be determined for which of the math statements shown below? State the letter of the correct answer.

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10) Use a calculator to determine the cube roots of the numbers shown below. State the answers in the same order as the problems are given from left to right.

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11) If the volume of a cube is 500 cubic meters, what is the length of one edge?

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12) Solve the following problems: (a) What is the greatest integer (x) that is less than the fourth root of 1000. (b) What is the smallest integer (y) that is greater than the fourth root of 1000? (c) What is the fourth root of 1000 rounded to the nearest hundredth?

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13) Which formula is used to calculate the volume of a right cylinder? State the letter of the correct answer.

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14) Find the amount of wax in a candle that has a radius of 1.5 inches and a height of 9 inches.

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15) A swimming pool has a diameter of 18 feet and a height of 4 feet. a) What is the volume of the swimming pool in cubic feet? (b) How many gallons of water are needed to fill the pool? (Note: The conversion factor is shown below.) Express both answers rounded to the nearest whole number.

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16) The radius of a fresh wheel of cheese is 3 inches and the height is 6 inches. (a) What is volume of the wheel of cheese? (b) If a wedge is cut from the wheel of cheese and the wedge forms a ninety-degree angle at the center, what is the volume of the cheese that would be left?

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17) In modern wells, casings are inserted to hold the water. If a casing has a length of 80 FEET and the inside diameter of the casing is 6 INCHES, answer the following questions: (a) To the nearest tenth of a cubic foot, how much water will the casing hold? (Hint: Make sure all units are expressed in feet before calculating the volume.) (b) To the nearest gallon, how many gallons of water will the casing hold? (Note: The conversion factor is provided in the picture below.)

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18) A cylindrical propane tank, 7 feet long, holds 500 gallons of propane gas. (a) If one gallon of propane gas is approximately equal to 0.13 cubic feet, what is the volume of the tank to the nearest cubic foot? (b) What is the radius of the tank to the nearest tenth of a foot? (c) What is the diameter of the tank to the nearest tenth of a foot?

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19) Which formula is used to calculate the volume of a right cone? State the letter of the correct answer.

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20) What is the volume of a right cone with a radius of 8 meters and a height of 15 meters?

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21) In an hour glass, sand falls into a cone-shaped pile. If the height of the sand is 5 inches and the radius is 4 inches, what is the volume of the pile of sand?

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22) A cone has a slant height of 24 inches and the height and radius are equal in measure. (a) What is the radius of the cone? (b) What is the height of the cone? (c) What is the volume of the cone?

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23) A silo shaped like the one shown below is a composite shape of a cylinder and a pyramid. If the silo is filled completely, what is its total storage capacity if the height is 60 feet and the cone-shaped portion has a height and radius of 15 feet? (Note: The height of the silo is 60 feet which is the combined height of the pyramid and the cylinder.)

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24) A frustum (truncated cone), and the formula for determining its volume, is shown below. The radius (r) of the frustum’s upper base is 9 feet. The radius (R) of the frustum’s lower base is 15 feet. The height of the frustum is 8 feet and the slant height of the frustum is 10 feet. What is the volume of the frustum? (Note: A common mistake for this solid is to call it a “frustrum”; however, the correct term is “frustum”.)

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25) The volume of a pyramid is equal to __________ of the volume of a prism with the same base area and height.

a.) 1/2

b.) 1/3

c.) 2/3

d.) 1/4

e.) none of the above

26) Which formula is used to calculate the volume of a right pyramid? State the letter of the correct answer.

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27) If the area of the base of the octagonal pyramid is 553.12 square feet and the height of the pyramid is 19 feet, what is its volume?

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28) The “Great Pyramid” in Egypt is approximately 147 meters high and 230 meters along the edge of its square base. To the nearest whole meter, the volume is about how many meters?

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29) Find the volume of the regular hexagonal pyramid shown below, and then answer the following questions: (a) What is the perimeter of the regular hexagonal base? (b) What is the measure of the apothem of the hexagonal base? (c) What is the area of the hexagonal base? (d) What is the volume of the pyramid?

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30) The length of the edge of the square base of a pyramid is six centimeters and the height of the pyramid is 21 centimeters. What is the volume of the space around the pyramid if it is enclosed in a rectangular prism with the same square base and the same height?

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31) Which of the following BEST describes the application of Cavalieri’s Principle?

a.) The volume of an oblique prism is the same as the volume of a right prism.

b.) The volume of an oblique cone is the same as the volume of a right cone.

c.) The volume of an oblique cylinder is the same as the volume of a right cylinder.

d.) The volume of an oblique pyramid is the same as the volume of a right pyramid.

e.) All of the above.

32) What is the volume of an oblique cone that has a radius of 6 centimeters and a height of 19 centimeters?

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33) What is the volume of an oblique cylinder that has a radius of 5 centimeters and a height of 22 centimeters?

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34) An oblique prism has a rectangular base that measures 10 inches by 8 inches and slanted edges that measure 12 inches. The slanted edge forms a 60-degree angle with the 10-inch edge as shown in the figure below. (a) What is the height? (Hint: Recall the relationship between the sides of a 30-60-90-degree right triangle.) (b) What is the volume of the oblique prism?

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35) Which formula is used to calculate the volume of a sphere? State the letter of the correct answer.

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36) What is the volume of a sphere with a radius of 10.4 centimeters?

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37) What is the volume of the globe portion of the snow globe shown below?

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38) The surface area of a sphere is 40,000 square feet. (a) What is the radius? (b) What is the volume of the sphere?

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39) The Sun is many times larger than the Earth. Let’s examine that ratio. Based on the lengths of the diameters given below, answer the following questions: (a) What is the volume of the Sun? Express the answer in terms of “pi”. (b) What is the volume of the Earth? Express the answer in terms of “pi”. (c) The Sun is how many times larger than the Earth? Round the answers to the nearest whole number. (Hint: Use your computer’s calculator if one is available.)

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40) Which statement BEST describes the pyramids?

a.) The pyramids are similar.

b.) The pyramids are congruent.

c.) The pyramids are neither similar nor congruent.

41) Which statement BEST describes the pyramids?

a.) The pyramids are similar.

b.) The pyramids are congruent.

c.) The pyramids are neither similar nor congruent.

42) Which statement BEST describes the spheres?

a.) The spheres are similar.

b.) The spheres are congruent.

c.) The spheres are both similar and congruent.

43) True or False. The cylinders are similar.

True

False

44) What is the scale factor between the lengths, widths, and heights of the two similar prisms? Compare Prism A to Prism B.

a.) 1 : 5

b.) 2 : 5

c.) 3 : 5

d.) 4 : 5

45) What is the surface area of (a) Prism A and (b) Prism B?

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46) Write a ratio that compares the surface area of Prism A to the surface area of Prism B. What is the SIMPLIFIED scale factor between the surface areas of the two prisms?

a.) 2 : 5

b.) 36 : 225

c.) 4 : 25

d.) 180 : 1125

47) What is the volume of (a) Prism A and (b) Prism B?

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48) Write a ratio that compares the volume of Prism A to the surface area of Prism B. What is the SIMPLIFIED scale factor between the volumes of the two prisms?

a.) 2 : 5

b.) 4: 25

c.) 8 : 125

d.) 200 : 3125

49) Look over the results of the previous problems. Compare the original scale factor, the simplified scale factor of the surface areas, and the simplified scale factor of the volumes. Complete the following statement. It is modeled from Theorem 29 and the results in the previous problems. If two solids are similar, with a scale factor of “a: b”, then the surface areas have a ratio that is the__________ of “a” and the __________ of “b”. The volumes have a ratio that is the __________of “a” and the __________ of “b”.

a.) square, cube, square, cube

b.) cube, square, cube, square

c.) cube, cube, square, square

d.) square, square, cube, cube

50) Pyramid A is similar to Pyramid B with a scale factor of 3 : 4. (a) If the surface area of Pyramid A is 350 square inches, what is the surface area of Pyramid B to the nearest whole square inch? (b) If the volume of Pyramid B is 1332 cubic inches, what is the volume of Pyramid A to the nearest whole cubic inch?

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