8-8 Volume and Surface Area of Composite Figures. Find the volume of the composite figure. Round to the nearest tenth if necessary.
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1 Find the volume of the composite figure. Round to the nearest tenth if necessary. The figure is made up of a triangular prism and a rectangular prism. Volume of triangular prism The figure is made up of two pyramids. Volume of top pyramid Volume of bottom pyramid m m 3 = m 3 The volume of the composite figure is about 2.3 cubic meters. 2.3 m 3 5 m m 3 = 13 m 3 The volume of the composite figure is 13 cubic meters. 13 m 3 esolutions Manual - Powered by Cognero Page 1
2 Find the surface area of the composite figure. Round to the nearest tenth if necessary. The figure is made up of a cube and a square pyramid. Surface area of bottom cube minus area where the two prisms connect The figure is made up of two rectangular prisms. Surface area of bottom rectangular prism minus area of bottom surface of top rectangular prism Surface area of top rectangular prism minus area of bottom surface Lateral surface area of top square pyramid 570 m m 2 = 720 m 2 The surface area of the composite figure is 720 m 2. The lateral area of the square pyramid is 600 ft 2. 2,000 ft ft 2 = 2,600 ft 2 The surface area of the composite figure is 2,600 ft 2. 2,600 ft m 2 Find the volume of the figure shown in cubic feet. esolutions Manual - Powered by Cognero Page 2
3 Find the volume of the figure shown in cubic feet. Round to the nearest tenth. Reason Inductively The swimming pool shown is being filled with water. Find the number of cubic feet that it will take to fill the swimming pool. (Hint: The area of a trapezoid is.) The figure is made up of a triangular prism and a rectangular prism. Convert all measurements to feet. 12 in. = 1 ft 5 in. = ft The swimming pool is made up of a rectangular prism and a trapezoidal prism. 10 in. = ft 24 in. = 2 ft Volume of triangular prism Volume of the trapezoidal prism. The bases are 8 ft and 3 feet, and the height is or 16 ft. 0.2 ft ft 3 = 0.5 ft 3 The volume of the composite figure is about 0.5 cubic feet. 1,344 ft 3 + 1,056 ft 3 = 2,400 ft 3 The volume of the swimming pool is 2,400 ft 3. 2,400 ft ft 3 The swimming pool shown is esolutions Manual - Powered by Cognero Page 3
4 Copy and Solve Show your work on a separate piece of paper. Round to the nearest tenth. Find the surface area of the figure shown. Find the volume of the figure shown. The figure is made up of a rectangular prism and a triangular prism. Surface area of bottom rectangular prism minus the area where the two prisms connect The figure is made up of two rectangular prisms. Volume of top rectangular prism Volume of bottom rectangular prism Surface area of top triangular prism but not the area where the two prisms connect The area of each triangle is or The area of the first rectangle is or The area of the second rectangle is or The sum of the areas of the sides is or 3.8 m m m 2 = 10.4 m 2 The surface area of the composite figure is 10.4 m m m 3 = 972 m 3 The volume of the composite figure is 972 cubic meters. 972 m 3 A carryout container is shown. The bottom base is a 10.4 m 2 Find the volume of the figure shown. esolutions Manual - Powered by Cognero Page 4
5 A carryout container is shown. The bottom base is a 4-inch square and the top base is a 4-inch by 6-inch rectangle. The height of the container is 5 inches. Find the volume of food that it holds. The food container is made up of a rectangular prism and two triangular prisms. Volume of the rectangular prism 300 m 3 + 1,080 m 3 = 1,380 m 3 The volume of the house is 1,380 cubic meters. Surface area: The house is made up of a rectangular prism and a triangular prism. Surface area of bottom rectangular prism minus the top and bottom of the prism Volume of triangular prisms 80 in in 3 = 100 in in 3 Refer to the house shown. Find the surface area and volume of the house. Do not include the bottom of the house when calculating the surface area. Surface area of top triangular prism but not the area where the two prisms connect The area of each triangle is or 25. The area of the first rectangle is or The area of the second rectangle is or The sum of the areas of the sides is or m m m 2 = m 2 The surface area of the house is m 2. volume: 1,380 m 3 ; surface area: m 2 Jaime is covering the boxes shown in felt, including Volume: The house is made up of a triangular prism and a rectangular prism. Volume of triangular prism esolutions Manual - Powered by Cognero Page 5
6 Jaime is covering the boxes shown in felt, including the back and bottom. What is the total area to be covered with felt? A. 23 in 2 B. 117 in 2 C. 172 in 2 D. 1,260 in 2 The figure is made up of two rectangular prisms. Surface area of bottom rectangular prism minus area of bottom surface of top rectangular prism Surface area of top rectangular prism minus area of bottom surface 138 in in 2 = 172 in 2 The total area to be covered is 172 in 2. The answer is C. C esolutions Manual - Powered by Cognero Page 6
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