Then/Now You have already found the areas of rectangles and triangles. (Lesson 5–1) Find volumes of prisms.
Vocabulary volume The measure of space occupied by a three-dimensional region
Concept You notice on your formula sheet, there are two formulas, the one above and one for rectangular prisms below V=lwh
Example 1 Find the Volume of a Rectangular Prism Find the volume of the rectangular prism. V=lwhFormula for volume of a prism V=ℓ ● w ● hThe base is a rectangle, so B = ℓ ● w. V=25 ● 16 ● 8ℓ = 25, w = 16, h = 8 V=3200 cm 3 Simplify. Answer: The volume is 3200 cubic centimeters.
Example 1 Find the Volume of a Rectangular Prism Find the volume of the rectangular prism. V=lwhFormula for volume of a prism V=ℓ ● w ● h V=8 ● 5 ● 21ℓ = 8, w = 5, h = 21 V=840 ft 3 Simplify. Answer: The volume is 840 cubic feet 5 ft 8 ft 21 ft
A.A B.B C.C D.D Example 1 CYP A.11.5 ft 3 B.22.5 ft 3 C.45 ft 3 D.81 ft 3 Find the volume of the prism.
Example 2 Volume of a Triangular Prism Find the volume of the triangular prism. The height of the prism is 3 in. Answer: The volume is 15 cubic inches. V=BhFormula for volume of a prism V = 15Simplify. The base is a triangle, so.
A.A B.B C.C D.D Example 2 A.33.5 ft 3 B.30 ft 3 C.15 ft 3 D.10.5 ft 3 Find the volume of the triangular prism.
Example 4 Find the volume of the solid. A. 262 m 3 B. 972 m 3 C. 918 m 3 D. 1458 m 3 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 V = ℓwh V = Bh Answer: The answer is D. Solve the Test Item V = 972 V = 486 The volume of the figure is 972 + 486 or 1458 cubic meters. V = 12 ● 9 ● 9
A.A B.B C.C D.D Example 4 A.1492 in 3 B.932 in 3 C.896 in 3 D.718 in 3 Find the volume of the solid.
Example 3 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? Answer: The height of the batter is 3 inches. V=BhFormula for volume of a prism V= ℓ ● w ● hReplace B with ℓ ● w. 192=8 ● 8 ● hReplace V with 192, ℓ with 8, and w with 8. 192=64hSimplify. 3=hDivide each side by 64.
A.A B.B C.C D.D Example 3 A.2 feet B.4 feet C.8 feet D.30 feet 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.