Teacher Page Geometry / Day #12 Surface Area 45 Minutes 9-12.G.1.3 Draw three-dimensional objects and calculate the surface areas and volumes of these figures (e.g. prisms, cylinders, pyramids, cones, spheres) as well as figures constructed from unions of prisms with faces in common, given the formulas for these figures. 1. Find the surface area of the prism. 3 in. 9 in. 24 in. a. 315 in 2 b. 630 in 2 c. 450 in 2 d. 820 in 2 2. Find the surface area of the cylinder, with a radius of 4 in. and height of 7 in. a. 125 in 2 b. 304 in 2 c. 276 in 2 d. 510 in 2
3. If a box with dimensions of 10 in., 8 in., and 4 in. is to be wrapped in paper for a present. How many square inches of paper is needed for the entire box? How many rolls are needed? There are 24 square inches of paper per roll. 3. 4. Find the surface area of a sphere with volume 288 m 3. Give your answer in terms of. a. 144 m 2 c. 144 m 2 b. 6 m 2 d. 864 m 2
5. John wants to paint his bedroom. The dimensions are 14 ft. by 12 ft. and his ceiling is 8 ft. high. What is the area of the painted surfaces in his room, disregard windows and doors? If each gallon of paint covers 300 square feet, how many gallons will John need to buy? And, if each gallon of paint costs $16, how much will it costs John to paint his bedroom? 5.
Key for Teacher Page Geometry / Day #12 Surface Area 45 Minutes 1. Find the surface area of the prism. 3 in. 9 in. 24 in. a. 315 in 2 b. 630 in 2 (Correct Answer) c. 450 in 2 d. 820 in 2 Surface Area Rectangular Solid Formula: 2LW+ 2WH + 2LH 2*24*9 + 2*9*3 + 2*24*3 = 432 + 54 + 144 = 630 in 2 2. Find the surface area of the cylinder, with a radius of 4 in. and height of 7 in. a. 125 in 2 b. 304 in 2 c. 276 in 2 (Correct Answer) d. 510 in 2 Surface Area Cylinder Formula: 2 r 2 + 2 rh 2* *4 2 + 2 4*7 = 276 in 2
3. If a box with dimensions of 10 in., 8 in., and 4 in. is to be wrapped in paper for a present. How many square inches of paper is needed for the entire box? How many rolls are needed? There are 24 square inches of paper per roll. 3. Surface Area Rectangular Solid Formula: 2LW+ 2WH + 2LH 2*10*4 + 2*4*8 + 2*10*8 = 80 + 64 + 160 = 304 in 2 (1 Point) 304/24 = 12.6 rolls - need to buy 13 rolls (1 Point) 4. Find the surface area of a sphere with volume 288 m 3. Give your answer in terms of. a. 144 m 2 c. 144 m 2 (Correct Answer) b. 6 m 2 d. 864 m 2 Volume of a sphere 288 = (4/3) r 3 Substitute 288 for V. Radius = 6 Solve for r. Surface area of a sphere S = 4 62 Substitute 6 for r. A B C D Feedback Surface area has pi in its formula. Substitute the radius to solve for surface area. Correct! Solve for radius first.
5. John wants to paint his bedroom. The dimensions are 14 ft. by 12 ft. and his ceiling is 8 ft. high. What is the area of the painted surfaces in his room, disregard windows and doors? If each gallon of paint covers 300 square feet, how many gallons will John need to buy? And, if each gallon of paint costs $16, how much will it costs John to paint his bedroom? 5. Surface Area Rectangular Solid Formula: LW+ 2WH + 2LH (note: floor is not painted) 14*12 + 2*12*8 + 2*14*8 = 168 + 192 + 224 = 584 ft 2 area of painted surface in room (2 Points) 584/300 = 1.95 gallons need to buy 2 gallons (1 Point) 2 gallons x $16 = $32 to paint John s room (1 Point)
Name: Date: Per: Student Page: Geometry/ Day #12 Surface Area 1. Find the surface area of the prism. 4 in 2 in a. 56 in 2 b. 144 in 2 c. 112 in 2 d. 176 in 2 8 in 2. Find the surface area of the right cylinder. Give your answer in terms of. 6m 10 m a. 132 m 2 b. 69 m 2 c. 60 m 2 c. 78 m 2
3. The radius and slant height of the right cone are multiplied by. Describe the effect on the surface area. 12 cm 4 cm a. The surface area is multiplied by. b. The surface area is multiplied by. c. The surface area is multiplied by. d. The surface area is multiplied by. 4. Square cake pans 20 cm on an edge and 6 cm deep are to be coated on the inside with a non-stick material. What is the total area that will need coating for each pan? If the amount of non-stick material available covers 100m 2, how many pans can be coated? 4.
5. A box is 12 inches in width, 16 inches in length, and 6 inches in height. How many square inches of paper would be required to cover it on all sides? a. 192 b. 360 c. 720 d. 900 6. Find the surface area in square inches of a cylinder with a diameter of 5 inches and a height of 10 inches. Use 3.14 for. Round to the nearest tenth. a. 196.3 in 2 b. 173.7 in 2 c. 157 in 2 d. 53.1 in 2 7. The length, width, and height of the right rectangular prism are tripled. Describe the effect on the surface area. 3 in. 9 in. 24 in. a. The surface area is multiplied by 3. b. The surface area is multiplied by 9. c. The surface area is multiplied by 27. d. The surface area is multiplied by 81.
8. A commercial walk in refrigerator with outside dimensions of 8 ft. high by 24. ft long by 7 ft. wide is to be painted. Its walls, floor, and ceiling are 3 in. thick. Inside, all four walls, the floor, and the ceiling are to be painted. Outside, only the four walls are to be painted. What is the total area inside that needs to be painted? What is the total area outside that needs to be painted? How many gallons of paint are needed if one gallon of paint covers 300 sq ft? 8.
Key Student Page Geometry / Day #12 Surface Area 1. Find the surface area of the prism 4 in 2 in a. 56 in 2 8 in b. 144 in 2 c. 112 in 2 (Correct Answer) d. 176 in 2 SA rectangular prism Formula: SA=2LW+ 2WH + 2LH 2*8*4 + 2*4*2 + 2*8*2 = 64 + 16 + 32 = 112 in 2 2. Find the surface area of the right cylinder. Give your answer in terms of. 6m 10 m a. 132 m 2 b. 69 m 2 c. 60 m 2 c. 78 m 2 (Correct Answer) SA = 2 r 2 + 2 rh SA = 2( )(3 2 ) + 2( )(3)(10) Substitute radius (radius is half of diameter)and height SA = 18 + 60 SA = 78
3. The radius and slant height of the right cone are multiplied by. Describe the effect on the surface area. 12 cm 4 cm a. The surface area is multiplied by. b. The surface area is multiplied by. (Correct Answer) c. The surface area is multiplied by. d. The surface area is multiplied by. Original dimensions: Radius and slant height multiplied by : The surface area is multiplied by. A B C D Feedback When the radius of the base is multiplied by one-third, the area of the base is multiplied by oneninth. Correct! Find the surface area of both cones and compare them. Find the surface area of both cones and compare them.
4. Square cake pans 20 cm on an edge and 6 cm deep are to be coated on the inside with a non-stick material. What is the total area that will need coating for each pan? If the amount of non-stick material available covers 100m 2, how many pans can be coated? 4. SA rectangular prism (note: no top on cake pan, therefore only one dimension of L x W) Formula: SA=LW+ 2WH + 2LH SA=20x20 + 2*20*6 + 2*20*6 SA=400 + 240 + 240 SA= 880 cm 2 (1 point) 880 / 100 = 8.8 8 pans can be coated (1 point) 5. A box is 12 inches in width, 16 inches in length, and 6 inches in height. How many square inches of paper would be required to cover it on all sides? a. 192 b. 360 c. 720 (Correct Answer) d. 900 SA rectangular prism SA=2LW+ 2WH + 2LH SA=2*16*12 + 2*12*6 + 2*16*6 SA= 384 + 144 + 192 SA = 720 6. Find the surface area in square inches of a cylinder with a diameter of 5 inches and a height of 10 inches. Use 3.14 for. Round to the nearest tenth. a. 196.3 in 2 (Correct Answer) b. 173.7 in 2 c. 157 in 2 d. 196.2 in 2 SA = 2 r 2 + 2 rh SA = 2( )(2.5 2 ) + 2( )(2.5)(10) Substitute radius (radius is half of diameter)and height SA = 39.25 + 157 SA = 196.3 in 2
7. The length, width, and height of the right rectangular prism are tripled. Describe the effect on the surface area. 3 in. 9 in. 24 in. a. The surface area is multiplied by 3. b. The surface area is multiplied by 9. (Correct Answer) c. The surface area is multiplied by 27. d. The surface area is multiplied by 81. Surface Area Rectangular Solid Compare the surface areas. 5670 = 9 630 Formula: 2LW+ 2WH + 2LH Surface Area Original 2*24*9 + 2*9*3 + 2*24*3 = 432 + 54 + 144 = 630 in 2 Surface Area Tripled 2*72*27 + 2*27*9 + 2*72*9=3888 + 486 + 1296 = 5670 in 2 When the length, width, and height are tripled, the surface area is multiplied by 3 2, or 9.
8. A commercial walk in refrigerator with outside dimensions of 8 ft. high by 24. ft long by 7 ft. wide is to be painted. Its walls, floor, and ceiling are 3 in. thick. Inside, all four walls, the floor, and the ceiling are to be painted. Outside, only the four walls are to be painted. What is the total area inside that needs to be painted? What is the total area outside that needs to be painted? How many gallons of paint are needed if one gallon of paint covers 300 sq ft? 8. What is the total area inside that needs to be painted? Before the SA formula can be applied each outside measurement must be reduced by 6 inches since the walls are each 3 inches thick, to get the inside measurements. Inside measurements: 7.5 ft. high, 23.5 ft. long, 6.5 ft. wide. SA=2LW+ 2WH + 2LH SA=2*23.5*6.5 + 2*6.5*7.5 + 2*23.5*7.5 SA=305.5 + 97.5 + 352.5 = 755.5 ft 2 (2 points) What is the total area outside that needs to be painted? Note: Only the four walls are to be painted outside. SA=2WH + 2LH SA=2*7*8 + 2*24*8 = 112 + 384 = 496 ft 2 ft 2 (1 point) How many gallons of paint are needed if one gallon of paint covers 300 sq ft? 755.5 + 496 = 1251.5 / 300 = 4.17 need to purchase 5 gallons (1 point)