8 8 Volume and Surface Area of Composite Figures

8-8 Volume and Surface Area of Composite Figures Find the volume of the composite figure. Round to the nearest tenth if necessary.

2.

SOLUTION: The figure is made up of two pyramids. Volume of top pyramid

Volume of bottom pyramid

5 m3 + 8 m3 = 13 m3 The volume of the composite figure is 13 cubic meters. ANSWER: 13 m3

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8-8 Volume and Surface Area of Composite Figures Find the surface area of the composite figure. Round to the nearest tenth if necessary.

4.

SOLUTION: 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

570 m2 + 150 m2 = 720 m2 The surface area of the composite figure is 720 m2. ANSWER: 720 m2

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8-8 Volume and Surface Area of Composite Figures

6. 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

.)

SOLUTION: The swimming pool is made up of a rectangular prism and a trapezoidal prism. Volume of rectangular prism

Volume of the trapezoidal prism. The bases are 8 ft and 3 feet, and the height is 30 ? 14 or 16 ft.

1,344 ft3 + 1,056 ft3 = 2,400 ft3 The volume of the swimming pool is 2,400 ft3. ANSWER: 2,400 ft3

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8-8 Volume and Surface Area of Composite Figures Copy and Solve Show your work on a separate piece of paper. Round to the nearest tenth.

8. Find the volume of the figure shown.

SOLUTION: The figure is made up of two rectangular prisms. Volume of top rectangular prism

Volume of bottom rectangular prism

108 m3 + 864 m3 = 972 m3 The volume of the composite figure is 972 cubic meters. ANSWER: 972 m3

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8-8 Volume and Surface Area of Composite Figures

10. 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.

SOLUTION: Volume: The house is made up of a triangular prism and a rectangular prism. Volume of triangular prism

Volume of rectangular prism

300 m3 + 1,080 m3 = 1,380 m3 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

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 7.1 ? 12 or 85.2. The area of the second rectangle is 7.1 ? 12 or 85.2. The sum of the areas of the sides is 25 + 25 + 85.2 + 85.2 or 220.4 m2. 396 m2 + 220.4 m2 = 616.4 m2 The surface area of the house is 616.4 m2.

ANSWER: volume: 1,380 m3 surface area: 616.4 m2

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