Practice: Surface Area and Volume

Practice: surface area and volume

Multiple Choice

Identify the choice that best completes the statement or answers the question.

____1.Determine the surface area of this regular tetrahedron to the nearest square centimetre.

a. / 116 cm2 / b. / 44 cm2 / c. / 58 cm2 / d. / 29 cm2

____2.The lateral area of a cone is 198.6 cm2. The diameter of the cone is 10.2 cm. Determine the height of the cone to the nearest tenth of a centimetre.

a. / 12.4 cm / b. / 8.0 cm / c. / 8.8 cm / d. / 11.3 cm

____3.The slant height of a right square pyramid is 17 ft. and the side length of the base is 13 ft. Determine its lateral area to the nearest square foot.

a. / 111 square feet / b. / 408 square feet / c. / 884 square feet / d. / 442 square feet

____4.A regular tetrahedron has edge length 19.0 m and a slant height of 16.5 m. Calculate the surface area of the tetrahedron to the nearest square metre.

a. / 470 m2 / b. / 627 m2 / c. / 157 m2 / d. / 1254 m2

____5.A right cone has a height of 16 in. and a base diameter of 8 in. Determine the lateral area of the cone to the nearest square inch.

a. / 201 square inches / c. / 207 square inches
b. / 258 square inches / d. / 225 square inches

____6.In 2008, the Queen Sesheshet Pyramid was discovered in Egypt. Archeologists determined that the original height of this right square pyramid was about 14 m and the original base side length was about 22 m. Determine its original lateral area to the nearest square metre.

a. / 1267 m2 / b. / 783 m2 / c. / 196 m2 / d. / 616 m2

____7.A right rectangular pyramid has base dimensions 8 ft. by 6 ft. and a height of 12 ft. Calculate the surface area of the pyramid to the nearest square foot.

a. / 216 square feet / b. / 159 square feet / c. / 271 square feet / d. / 223 square feet

____8.A right pyramid has a square base with side length 12 m and a height of 7 m. Calculate the surface area of the pyramid to the nearest square metre.

a. / 365 m2 / b. / 443 m2 / c. / 664 m2 / d. / 312 m2

____9.The surface area of a right cone is 400.2 m2. The radius of the cone is 6.0 m. Determine the height of the cone to the nearest metre.

a. / 13 m / b. / 14 m / c. / 16 m / d. / 15 m

____10.A right cone has a height of 13 cm and a base diameter of 17 cm. Determine the surface area of the cone to the nearest square centimetre.

a. / 1057 cm2 / b. / 642 cm2 / c. / 574 cm2 / d. / 415 cm2

____11.Calculate the slant height, s, of this right square pyramid to the nearest tenth of a centimetre.

a. / 6.1 cm / b. / 16.6 cm / c. / 12.1 cm / d. / 11.9 cm

____12.Calculate the edge length, l,of this regular tetrahedron to the nearest tenth of a metre.

a. / 10.6 m / b. / 5.3 m / c. / 7.1 m / d. / 6.5 m

____13.Calculate the volume of this right square pyramid to the nearest cubic foot.

a. / 54 cubic feet / b. / 163 cubic feet / c. / 62 cubic feet / d. / 58 cubic feet

____14.Calculate the volume of this right rectangular pyramid to the nearest cubic inch.

a. / 64 cubic inches / b. / 72 cubic inches / c. / 216 cubic inches / d. / 78 cubic inches

____15.Calculate the volume of this right cone to the nearest tenth of a cubic metre.

a. / 47.1 m3 / b. / 49.3 m3 / c. / 141.4 m3 / d. / 55.0 m3

____16.A regular tetrahedron has base area 146.4 m2 and height 10.7 m. Determine its volume to the nearest cubic metre.

a. / 522 m3 / b. / 1566 m3 / c. / 586 m3 / d. / 3133 m3

____17.A right rectangular prism with base dimensions 7.8 m by 5.1 m has a volume of 110.1 m3. Determine the height of the prism to the nearest tenth of a metre.

a. / 8.3 m / b. / 1.2 m / c. / 5.5 m / d. / 2.8 m

____18.A right rectangular pyramid has base dimensions 9 ft. by 5 ft., and a height of 12 ft. Determine its volume to the nearest cubic foot.

a. / 237 cubic feet / b. / 192 cubic feet / c. / 180 cubic feet / d. / 184 cubic feet

____19.A right cone has a height of 8 cm and a volume of 250 cm3. Determine the radius of the base of the cone to the nearest centimetre.

a. / 5 cm / b. / 11 cm / c. / 3 cm / d. / 17 cm

____20.A right cone has slant height 15 in. and base diameter 12 in. Determine its volume to the nearest cubic inch.

a. / 543 cubic inches / b. / 518 cubic inches / c. / 1555 cubic inches / d. / 396 cubic inches

____21.A right square pyramid has a base side length of 11 ft. and a slant height of 19 ft. Calculate the volume of the pyramid to the nearest cubic foot.

a. / 2201 cubic feet / b. / 539 cubic feet / c. / 766 cubic feet / d. / 734 cubic feet

____22.This regular tetrahedron has a height of 4.7 cm. Calculate its volume to the nearest cubic centimetre.

a. / 23 cm3 / b. / 68 cm3 / c. / 58 cm3 / d. / 45 cm3

____23.This right square pyramid has a volume of 254.7 cm3. Calculate the side length of its base, x, to the nearest tenth of a centimetre.

a. / 5.9 cm / b. / 4.3 cm / c. / 7.2 cm / d. / 4.1 cm

____24.A right cylindrical can has a volume of 263.1 cm3. What is the volume of a right cone with the same base and the same height, to the nearest tenth of a centimetre?

a. / 131.6 cm / b. / 89.7 cm / c. / 91.7 cm / d. / 87.7 cm

____25.The volume of this right cone is 14.7 mm3. Calculate its height, h, to the nearest tenth of a millimetre.

a. / 4.1 mm / b. / 2.8 mm / c. / 1.4 mm / d. / 1.0 mm

____26.A right square pyramid has a base side length of 4.5 cm and a slant height of 6.1 cm. Determine the volume of the pyramid to the nearest cubic centimetre.

a. / 13 cm3 / b. / 38 cm3 / c. / 43 cm3 / d. / 71 cm3

____27.The radius of a volleyball is approximately 11 cm. Determine the surface area of a volleyball to the nearest square centimetre.

a. / 1521 cm2 / b. / 380 cm2 / c. / 6082 cm2 / d. / 5575 cm2

____28.The surface area of a tennis ball is approximately 23 square inches. What is the diameter of the tennis ball to the nearest inch?

a. / 3 in. / b. / 4 in. / c. / 6 in. / d. / 1 in.

____29.Mars approximates a sphere with radius 2100 mi. What is the approximate volume of Mars?

a. / mi.3 / b. / mi.3 / c. / mi.3 / d. / mi.3

____30.A hemisphere has radius 11.6 cm. What is the surface area of the hemisphere to the nearest tenth of a square centimetre?

a. / 3269.1 cm2 / b. / 918.4 cm2 / c. / 845.5 cm2 / d. / 1268.2 cm2

____31.A hemisphere has radius 11.4 cm. What is the volume of the hemisphere to the nearest tenth of a cubic centimetre?

a. / 6205.9 cm3 / b. / 3102.9 cm3 / c. / 1224.8 cm3 / d. / 1633.1 cm3

____32.A ten-pin bowling ball has a radius of approximately in. Determine the surface area of the ball to the nearest square inch.

a. / 57 square inches / c. / 227 square inches
b. / 908 square inches / d. / 322 square inches

____33.A ten-pin bowling ball has a radius of approximately in. Determine the volume of the ball to the nearest cubic inch.

a. / 5642 cubic inches / c. / 322 cubic inches
b. / 2572 cubic inches / d. / 227 cubic inches

____34.A sphere has a surface area of 6.4 m2. What is the diameter of the sphere to the nearest tenth of a metre?

a. / 2.3 m / b. / 1.4 m / c. / 2.0 m / d. / 0.7 m

____35.A sphere has a surface area of 10.1 m2. What is the radius of the sphere to the nearest tenth of a metre?

a. / 3.7 m / b. / 4.8 m / c. / 1.8 m / d. / 0.9 m

____36.The circumference of a beach ball is 55 cm. Determine its volume to the nearest cubic centimetre.

a. / 963 cm3 / b. / 2810 cm3 / c. / 22 476 cm3 / d. / 307 cm3

____37.The circumference of a medicine ball is 28 in. Determine its surface area to the nearest square inch.

a. / 371 square inches / c. / 998 square inches
b. / 111 square inches / d. / 250 square inches

____38.A stadium has a roof that approximates a hemisphere with circumference 2500 ft. Determine the surface area of the roof to the nearest square foot.

a. / 1 492 078 square feet / c. / 994 718 square feet
b. / 3 978 874 square feet / d. / 131 928 625 square feet

____39.A flat basketball is inflated using a hand pump. The pump inflates the ball at a rate of

230 cm3 per pump, to a diameter of 23.5 cm. How many pumps are required to inflate the ball?

a. / 27 pumps / b. / 30 pumps / c. / 29 pumps / d. / 28 pumps

____40.A china bowl approximates a hemisphere with diameter 27.0 cm. What is the capacity of the bowl to the nearest tenth of a litre? (1000 cm3 = 1L)

a. / 5.2 L / b. / 10.3 L / c. / 0.4 L / d. / 2.6 L

____41.A china bowl approximates a hemisphere with diameter 30 cm. One cup is 250 mL. How many cups are required to completely fill the bowl?

a. / 30 cups / b. / 28 cups / c. / 9 cups / d. / 29 cups

Short Answer

42.A right cone has a slant height of 14 in. and a base diameter of 10 in. Determine the surface area of the cone to the nearest square inch.

43.A regular tetrahedron with edge length 12.7 mm has a surface area of 229.0 mm2. Determine the slant height of the tetrahedron to the nearest millimetre.

44.A right square pyramid has a height of 15 cm and a slant height of 17 cm. Determine the side length of the base of the pyramid to the nearest centimetre.

45.A regular tetrahedron has an edge length of 9.0 m and a slant height of 7.8 m. Calculate the surface area of the tetrahedron to the nearest tenth of a square metre.

46.In 2008, the Queen Sesheshet Pyramid was discovered in Egypt. Archeologists determined that the original height of this right square pyramid was about 14 m and the original base side length was about 22 m. Determine its original volume to the nearest cubic metre.

47.A regular tetrahedron has base area 98.9 m2 and height 8.6 m. Determine its volume to the nearest tenth of a cubic metre.

48.A right rectangular pyramid has base dimensions 11 cm by 7 cm and height 9 cm. Determine the volume of the pyramid to the nearest cubic centimetre.

49.A right cone has a diameter of 17.1 cm and a height of 11.3 cm. Determine the volume of the cone to the nearest tenth of a cubic centimetre.

50.A right pyramid has a base that is a regular hexagon with side length 2.0 cm. The pyramid has a height of 5.3 cm and a base area of 10.4 cm2. Calculate the volume of the pyramid to the nearest tenth of a cubic centimetre.

51.A right cone has a volume of 871 cubic inches. The radius of the cone is 8 in. Determine the height of the cone to the nearest inch.

52.Determine the surface area of this sphere to the nearest square centimetre. Determine its volume to the nearest cubic centimetre.

53.Determine the surface area of this sphere to the nearest square inch. Determine its volume to the nearest cubic inch.

54.A hemisphere has radius 7 ft. Determine the surface area of the hemisphere to the nearest square foot.

55.A hemisphere has radius 12 m. Determine the volume of the hemisphere to the nearest tenth of a cubic metre.

56.A spherical balloon has a surface area of 88 cm2. What is the diameter of the balloon to the nearest tenth of a centimetre?

57.A spherical globe has diameter 41.3 cm. What is the volume of the globe to the nearest tenth of a centimetre?

Problem

58.A right pyramid with a base that is a regular hexagon has a slant height of 5.0 m. The base area is 10.4 m2 and the side length of the base is 2.0 m. Calculate the surface area of the pyramid to the nearest tenth of a square metre.

59.Three wooden blocks need to be painted. The first block is a right rectangular pyramid with base dimensions 1.5 cm by 2.5 cm and a height of 2.0 cm . The second block is a right square pyramid with a base length of 2.8 cm and a height of 2.0 cm. The third block is a right cone with a height of 2.0 cm and a base diameter of 3.6 cm. Which block requires the most paint? Which block requires the least paint? Sketch diagrams to help explain your answer.

60.Nicole has this right cone, which has lateral area 414.5 cm2. She needs a cone with height at least 15.5 cm for a craft project. Is this cone tall enough? Justify your answer.

61.A right rectangular pyramid has base dimensions 6 cm by 4 cm and a height of 8 cm. Determine its lateral area to the nearest square centimetre.

62.A right square pyramid has a height of 7.5 m and a base perimeter of 36 m. Calculate the surface area of the pyramid to the nearest square metre.

63.A right square pyramid has base perimeter 62.4 m and height 6.4 m. Calculate the volume of the pyramid to the nearest cubic metre.

64.A right rectangular pyramid has base dimensions 23.2 cm by 17.0 cm and volume 1552.4 cm3. Calculate the height of the pyramid to the nearest tenth of a centimetre.

65.A right cylinder has base radius 22.9 cm and height 17.1 cm. Determine the volume of a right cone with the same base and the same height, to the nearest tenth of a cubic centimetre.

66.Francis has three empty containers: a right rectangular prism, a right square pyramid, and a right cone. Each container has height 2.0 cm. The prism has base dimensions 1.5 cm by 2.5 cm. The pyramid has base side length 3.4 cm. The cone has base diameter 3.8 cm. Determine the volume of each container to the nearest tenth of a cubic centimetre. Which container has the least volume? Which container has the greatest volume? Explain your answer.

67.Determine the volume of a right prism that has the same base and the same height as the right square pyramid below. Give your answer to the nearest tenth of a cubic metre. Explain your answer.

68.A right cone has a base diameter of 8 in. and a volume of 259 cubic inches. Determine the slant height of the cone to the nearest inch.

69.A candle approximates a sphere with circumference 21 cm. The surface of the candle is to be covered with glitter.

a) Determine the radius of the candle to the nearest centimetre.

b) Determine the surface area of the candle to the nearest square centimetre.

70.A hemisphere has radius 23.3 m.

a) Determine the surface area of the hemisphere to the nearest tenth of a square metre.

b) Determine the volume of the hemisphere to the nearest tenth of a cubic metre.

71.A sphere has a diameter of 24 in. A hemisphere has a radius of 18 in. Franco says the surface area of the sphere is greater than the surface area of the hemisphere. Do you agree? Justify your answer.

72.A baby’s rattle contains a plastic ball inside a spherical case. The diameter of the plastic ball is 2 cm and the diameter of the case is 7 cm.

a) Calculate the volume of the spherical case, to the nearest cubic centimetre.

b) Calculate the volume of the plastic ball, to the nearest cubic centimetre.

c) Calculate the volume of air in the rattle, to the nearest cubic centimetre.

73.A pail of ice cream is cylindrical, with diameter 10 in. and height 12 in. A scoop makes a sphere of ice cream with diameter 2 in. How many full scoops of ice cream can be made from this pail?

Practice: surface area and volume

Answer Section

MULTIPLE CHOICE

1.ANS:CPTS:1DIF:Easy

REF:1.4 Surface Areas of Right Pyramids and Right ConesLOC:10.M3