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Volumes of Pyramids & Cones Objectives: 1) Find the volume of a right Pyramid. 2) Find the volume of right Cone.

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Finding Volumes of Pyramids and Cones In Lesson 12.4, you learned that the volume of a prism is equal to Bh, where B is the area of the base, and h is the height. In Lesson 12.4, you learned that the volume of a prism is equal to Bh, where B is the area of the base, and h is the height. From the figure at the left, it is clear that the volume of the pyramid with the same base area B and the same height h must be less than the volume of the prism. The volume of the pyramid is one third the volume of the prism.

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I. Volume of a Pyramid Pyramid – Is a polyhedron in which one face can be any polygon & the other faces are triangles. Pyramid – Is a polyhedron in which one face can be any polygon & the other faces are triangles. h V p = Bh Area of the Base A = lw A = ½bh Height of the pyramid, not to be confused with the slant height (l)

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Ex.1: Volume of a right Pyramid Find the volume of a square pyramid with base edges of 10cm & a height of 20cm. Find the volume of a square pyramid with base edges of 10cm & a height of 20cm. 20cm 10cm

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Ex.2: Another square pyramid Find the area of a square pyramid w/ base edges 10ft long & a slant height 13ft. Find the area of a square pyramid w/ base edges 10ft long & a slant height 13ft. h 13ft 10ft 5ft V = ()Bh = () 100h = ()100___ = ()1200 = 400ft 3 a 2 + b 2 = c 2 h = 13 2 h 2 = 144 h = 12 12

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II. Volume of a Cone Cone – Is pointed like a pyramid, but its base is a circle. Cone – Is pointed like a pyramid, but its base is a circle. h r V c = Bh Area of the Base A = r 2

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Ex.3: Find the volume of the following right cone w/ a diameter of 6in. 11in Circle 3in

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Ex.4: Volume of a Composite Figure 8cm 10cm 4cm Volume of Cylinder NEXT! V = Bh = r 2 h = (8) 2 (4) = 256

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Ex.5: Solve for the missing variable. The following cone has a volume of 110. What is its radius. The following cone has a volume of 110. What is its radius. 10cm r V = Bh V = ( r 2 )h 110 = () r 2 (10) 11 = ()r 2 33 = r 2 r = 33 cm

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What have we learned??? Volume of Cones & Pyramids Volume of Cones & Pyramids h h r V c = Bh Area of Base Height is the actual height of the solid not the slant height!!!

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