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Find the volumes of pyramids and cones Objective Find the volumes of pyramids and cones Volume of pyramid Volume of cone Example 6-3b

A three-dimensional figure with one circular base Vocabulary Cone A three-dimensional figure with one circular base Example 6-3b

Vocabulary Pyramid A polyhedron with one base that is a polygon and faces that are triangles Example 6-3b

Example 1 Find the Volume of a Pyramid Example 2 Use Volume to Solve a Problem Example 3 Find the Volume of a Cone Lesson 6 Contents

Find the volume of the pyramid. Volume = (Area of base)  Height of Pyramid Volume = (L  W)  Height of Pyramid Replace formula for rectangle in “area of base” Volume = (7 cm  3 cm)  20 cm Replace L with 7 cm Replace W with 3 cm Replace Height of Pyramid with 20 cm 1/3 Example 6-1a

Find the volume of the pyramid. Volume = (Area of base)  Height of Pyramid Volume = (L  W)  Height of Pyramid Volume = (7 cm  3 cm)  20 cm Since multiplication is the only process, multiply all numbers Answer: Volume = 140 cm3 Multiply the units of measure 1/3 Example 6-1a

Find the volume of the pyramid. Answer: Volume = 80 m3 1/3 Example 6-1b

Write formula for volume of a pyramid SOUVENIRS A novelty souvenir company wants to make snow “globes” shaped like a pyramid. It decides that the most cost-effective maximum volume of water for the pyramids is 12 cubic inches. If a pyramid globe measures 4 inches in height, find the area of its base. V = Bh Write formula for volume of a pyramid 12 in3 =  B  4 in Replace V with 12 in3 Define variable as B which is area of base Replace h with 4 in 2/3 Example 6-2a

Ask “What is being done to the variable?” V = Bh 2 things: Multiplied by 4 and 12 in3 =  B  4 in Do the inverse of one at a time 12 in3 =  B  4 in Bring down entire equation 4 in 4 in Using a fraction bar, divide both sides by 4 in 3 in2 =  B Combine “like” terms 2/3 Example 6-2a

Ask “What is being done to the variable?” Do the inverse of one at a time 3 in2 =  B Bring down entire equation Using a fraction bar, divide both sides by Answer: 9 in2 = B Combine “like” terms Remember: B = Area of Base! 2/3 Example 6-2a

TOYS A company is designing pyramid shaped building blocks with a square base. They want the volume of the blocks to be 18 cubic inches. If the length of the side of the base is 3 inches, what should be the height of the blocks? Answer: H = 6 in. 2/3 Example 6-2c

Find the volume of the cone. Round to the nearest hundredth. Write formula for area of cone (1.5 m)2  8 m Replace r with 1.5 m 2.25 m2  8 m Replace h with 8 m Follow order of operations P E MD AS Evaluate the exponent 3/3 Example 6-3a

Find the volume of the cone. Round to the nearest hundredth. Since multiplication is the only process, multiply all numbers (1.5 m)2  8 m 2.25 m2  8 m Multiply the units Answer: V = 18.85 m3 3/3 Example 6-3a

Find the volume of the cone. Round to the nearest hundredth. * Find the volume of the cone. Round to the nearest hundredth. Answer: V = 37.70 in3 3/3 Example 6-3b

Volume of Pyramids and Cones Assignment Lesson 7:6 Volume of Pyramids and Cones 3 - 15 All End of Lesson 6