Geometry Chapters 12 &13 Surface Area and Volume Name: Period:
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1 Geometry Chapters 12 &13 Surface Area and Volume Name: Period:
2 Area, Surface area, and Volume 2 and 3-Dimensional figures TYPE FIGURE PERIMETER AREA SURFACE AREA VOLUME Triangle Rectangle, square parallelogram Trapezoid Regular polygon Circle PRISM CYLINDER PYRAMID CONE SPHERE
3 Surface Area and Volume of Prisms, Pyramids, Cones, Cylinders, and Spheres Worksheet # 1 1) 2) 3) 4)
4 5) 6) 7) 8)
5 9) 10) 11) 12)
6 Surface Area and Volume of Prisms, Pyramids, Cones, Cylinders, and Spheres Worksheet # 2 1) 2) 3) 4)
7 5) 6) 7) 8)
8 9) 10) 11) 12)
9 Surface Area and Volume of Prisms, Pyramids, Cones, Cylinders, and Spheres Worksheet # 3 1) 2) 3) 4)
10 5) 6) 7) 8)
11 9) 10) 11) 12)
12 Surface Area and Volume of Prisms, Pyramids, Cones, Cylinders, and Spheres Worksheet # 4 1) 2) 3) 4)
13 5) 6) 7) 8) d = w = 9) h =
14 Surface Area and Volume Review Name: 1.) A company packages breakfast cereal in the two sizes of right cylindrical containers shown below. The containers are similar in shape. How many cubic inches does the large container hold? a. 90 π cubic inches b. 135 π cubic inches c. 360 π cubic inches d. 540 π cubic inches 2.) A cube has a volume of 729 cm 3. What is the length of each edge of the cube? a. 9 cm b. 11 cm c cm d. 243 cm 3.) A triangular prism is shown in the diagram below. What is the volume of the prism? a. 33 cm 3 b. 42 cm 3 c. 49 cm 3 d. 84 cm 3 4.) Vermont cheddar cheese can be purchased in right circular cylinders called cheese wheels that are 9.5 inches in diameter and 5 inches tall that sell for $ New York sharp cheddar cheese also can be purchased on cylindrical cheese wheels that are 6 inches in diameter and 8 inches tall that sell for $95. Which wheel Vermont or New York is the better buy in terms of dollars per cubic inch? Show you work and explain how you arrived at you answer.
15 5.) An artist carved a sphere out of stone. The radius of the sphere is 0.93 meter. Which of the following is closest to the volume of the sphere? a m 3 b m 3 c m 3 d m 3 6.) The right square pyramid shown below has a base measuring 9 inches on each side and a height of 15 inches. What is the volume, in cubic inches, of the right square pyramid? a. 135 b. 405 c. 540 d ) Two containers in the shape of right circular cylinders are equal in height. The radius of the larger container is 3 times the radius of the smaller container. The volume of the larger container is how many times the volume of the smaller container? a. 3 b. 6 c. 9 d ) Which container below holds the most water? 9.) An inflated round balloon with radius r= 50 centimeters hold approximately 523,600 cubic centimeters of air. When the balloon is contracted such that the radius is the original size, what is the approximate volume of the partially deflated balloon? a x 10 4 cm 3 b x 10 5 cm 3 c x 10 5 cm 3 d x 10 5 cm 3
16 10.) Jim wants to make a sandbox for his daughter. The sandbox measures 4 feet long by 5 feet wide by 1 foot deep. He wants the sand to be only 6 inches deep. How much sand should Jim buy? a. 10 cubic feet b. 12 cubic feet c. 14 cubic feet d. 29 cubic feet 11.) If the height of a cylinder was tripled, but the area of the base remained the same, what would happen to the volume? a. The volume would double b. The volume would triple c. The volume would be four times greater d. The volume would be nine times greater 12.) Jerry has two fish tanks. One tank is shaped like a cylinder, and the other tank is shaped like a triangular prism, as shown below. Jerry estimates that the volume of tank 1 is about 750 cubic inches. Which statement best compares the volumes to the two fish tanks? a. Tank 2 has about the same volume as tank 1. b. Tank 2 has about one-third the volume of tank 1. c. Tank 1 has about twice the volume of tank 2. d. Tank 1 has about six times the volume of tank ) A cylinder has a volume of approximately cubic inches and a radius of 4 inches. What is its height? a in. b in. c in. d in. 14.) A right cylinder has a height of 10 inches. The base of the cylinder has a circumference of 6π inches. What is the lateral surface area of the cylinder? a. 30π square inches b. 60 π square inches c. 90 π square inches d. 360 π square inches 15.) A square pyramid has a volume of 32 cubic units. What would be the volume if the dimensions of the square base were doubled? a. The volume would be two times the original b. The volume would be three times the original c. The volume would be four times the original d. The volume would be eight times the original
17 16.) The cylindrical oil tank shown below is half full. How much oil is in the tank? Round the answer to the nearest cubic foot. a. 113 cubic feet b. 151 cubic feet c. 226 cubic feet d. 452 cubic feet 17.) Which of the following is closest to the total surface area of a sphere with a radius of 6 centimeters? a. 113 cm 2 b. 151 cm 2 c. 301 cm 2 d. 452 cm 2 18.) The right square pyramid represented below has a base edge of 6 inches and a height of 5 inches. What is the volume in cubic inches of the pyramid? a. 60 b. 90 c. 120 d ) The diagram below shows a company s current packaging of its plant food. If the company doubles the radius of its current packaging, what effect will this change have on the volume of the container? a. The volume will be one and a half times the original packaging volume. b. The volume will be twice the original packaging volume. c. The volume will be tree times the original packaging volume. d. The volume will be four times the original packaging volume. 20.) Packard Painting has been hired to paint all the bench seats in the bleachers at McDuffy Stadium. There are 29 sections of bleacher seats. Most sections have 21 benches, but 7 have only 19. Each bench is 48 feet long, ten inches wide and about an inch thick. You don t need to paint the bottoms of the benches or the supports. One gallon of paint covers about 500 square feet. Which of these is the best estimate of the amount of paint Packard should but for this job? a. 6 gallons b. 60 gallons c. 600 gallons d gallons
18 21.) The length of each edge of a cube is doubled. By what factor is the volume of the cube increased? a. 2 b. 4 c. 6 d ) A candy box is in the shape of a triangular prism. It has dimensions of w=5cm, x=4cm, and y=10cm. What is the volume of the candy box? a. 100 cm 3 b. 150 cm 3 c. 200 cm 3 d. 400 cm 3 23.) Constance bought a box to hold her jelly beans. The dimensions of the box are 6 inches by 2 inches by 1 inch. The jelly beans weigh a total of 36 ounces. If each cubic inch inside the box can hold two ounces, how many ounces of jelly beans will have to be left out of the box? a. 24 b. 18 c. 12 d ) To properly fill the aquarium shown below, the water level should be 1.5 inches from the top of the aquarium. If the aquarium is filled properly, how many cubic inches of water will it contain? Note: The figure is not drawn to scale. a. 1,285 cubic inches b. 2,772 cubic inches c. 2,907 cubic inches d. 3,366 cubic inches 25.) A swimming pool is 50 meters long, 25 meters wide, and 3 meters deep. A liter is the same as cubic meter. How many liters of water are needed to fill the pool? a. 375 liters b. 3,750 liters c. 375,000 liters d. 3,750,000 liters 26.) Use the figure below to answer the following question. What is the approximate surface area of the figure? a sq cm b sq cm c sq cm d sq cm
19 27.) The diagram represents a tower. The tower is in the shape of a cone on top of a cylinder. Which measurement is closest to the total volume of the tower? a. 2,200 cubic meters b. 2,600 cubic meters c cubic meters d. 10,500 cubic meters 28.) Garrett made a toy box for his younger sister. The inside of the entire toy box, including the lid, is 15 in. wide, 30 in. long and 12 in. tall. Garrett wants to line the inside, including the lid, with purple cloth. How many square feet of cloth should he buy? a ft 2 b ft 2 c ft 2 d ft 2 29.) Tyrone has a cylindrical fish tank. The tank is 50 centimeters high and has a radius of 10 centimeters. What is the approximate volume of the tank? a. 60 cubic centimeters b. 500 cubic centimeters c. 3,140 cubic centimeters d. 15,700 cubic centimeters 30.) A pile of sand is in the shape of a cone. The diameter of the base is 24 feet and the height is 10 feet. Which of these is the volume of the pile of sand? Round the answer to the nearest cubic foot. a. 126 cubic feet b. 251 cubic feet c. 1,508 cubic feet d. 6,032 cubic feet 31.) A candle in the shape of a right circular cylinder is pictured below. Based on the dimensions shown in the picture, which of the following is closest to the lateral surface area of the candle? a. 46 cm 2 b. 170 cm 2 c cm 2 d cm 2
20 32.) A rectangular prism has the dimensions shown below. What is the volume of the prism? a. 10 ft 2 b. 10 cm 2 c. 30 ft 3 d. 30 cm 3 33.) What is the volume left in the cylinder after the shaded cone region is removed? a. 1,024 π in 3 b. 1,536 π in 3 c. 2,048 π in 3 d. 4,096 π in 3 34.) Use the picture below to answer the following question. How many 1- in. cubes will completely fill the carton shown? a. 14 b. 33 c. 90 d ) The triangular prism below represents the shape of Sylvia s tent. What is the volume of the tent in cubic feet? a. 180 b. 241 c. 255 d ) The coffee can below is ¾ full. How much coffee is in the can? a. about 57 in 3 b. about 130 in 3 c. about 170 in 3 d. about 226 in 3
21 37.) A rectangular prism has a volume of 56 cubic feet. The rectangular prism has a length of 7 feet and a width of 4 feet. What is the height of the rectangular prism? a. 2 feet b. 11 feet c. 22 feet d. 28 feet 38.) Jaime s Ice Cream Store is making chocolate covered cones to sell for summer. About how much chocolate will be required to cover the outside of each cone? a square inches b square inches c square inches d square inches 39.) Each of two different-sized boxes is in the shape of a right rectangular prism. The volume of the larger box is 4 times the volume of the smaller box. The dimensions of the smaller box are represented below. Length; l Width: w Height: h Which of the following could represent the dimensions of the larger box? a. l, 4w, 4h b. 2l, 2w, h c. 2l, 2w, 4h d. 4l, 4w, 4h 40.) The right square pyramid has a base length of 4 inches and a slant height of 7 inches. What is the surface area of the pyramid? a. 28 square inches b. 44 square inches c. 56 square inches d. 72 square inches
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