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Presentation transcript:

Splash Screen

Find volumes of composite figures. You have already found the areas of rectangles and triangles. (Lesson 5–1) Find volumes of prisms. Find volumes of composite figures. Then/Now

volume – is the measure of space occupied by a three-dimensional region. It is measured in cubic units. Vocabulary

Concept

Find the volume of the rectangular prism. Find the Volume of a Rectangular Prism Find the volume of the rectangular prism. V = Bh Formula for volume of a prism V = (ℓ ● w)h The base is a rectangle, so B = ℓ ● w. V = (25 ● 16)8 ℓ = 25, w = 16, h = 8 V = 3200 Simplify. Answer: The volume is 3200 cubic centimeters. Example 1

Find the volume of the prism. A. 11.5 ft3 B. 22.5 ft3 C. 45 ft3 D. 81 ft3 Example 1 CYP

Find the volume of the triangular prism. Volume of a Triangular Prism Find the volume of the triangular prism. V = Bh Formula for volume of a prism The base is a triangle, so . The height of the prism is 3 in. V = 15 Simplify. Answer: The volume is 15 cubic inches. Example 2

Find the volume of the triangular prism. A. 33.5 ft3 B. 30 ft3 C. 15 ft3 D. 10.5 ft3 Example 2

V = Bh Formula for volume of a prism Find the Missing Length BAKING Cake batter is poured into a pan that is a rectangular prism with an 8-inch square base. If the cake batter occupies 192 cubic inches, what will be the height of the batter? V = Bh Formula for volume of a prism V = ℓ ● w ● h Replace B with ℓ ● w. 192 = 8 ● 8 ● h Replace V with 192, ℓ with 8, and w with 8. 192 = 64h Simplify. 3 = h Divide each side by 64. Answer: The height of the batter is 3 inches. Example 3

SWIMMING POOLS A swimming pool is filled with 960 cubic feet of water SWIMMING POOLS A swimming pool is filled with 960 cubic feet of water. The pool is a rectangular prism 20 feet long and 12 feet wide and is the same depth throughout. Find the depth of the water. A. 2 feet B. 4 feet C. 8 feet D. 30 feet Example 3

Find the volume of the solid. A. 262 m3 B. 972 m3 C. 918 m3 D. 1458 m3 Read the Test Item The solid is made up of a rectangular prism and a triangular prism. The volume of the solid is the sum of both volumes. Example 4

Rectangular Prism Triangular Prism Solve the Test Item Rectangular Prism Triangular Prism V = ℓwh V = Bh V = 12 ● 9 ● 9 V = 972 V = 486 The volume of the figure is 972 + 486 or 1458 cubic meters. Answer: The answer is D. Example 4

Find the volume of the solid. A. 1492 in3 B. 932 in3 C. 896 in3 D. 718 in3 Example 4

End of the Lesson