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

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. 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.

Vp = ⅓Bh I. Volume of a Pyramid Pyramid – Is a polyhedron in which one face can be any polygon & the other faces are triangles. Vp = ⅓Bh h Area of the Base A = l•w A = ½bh Height of the pyramid, not to be confused with the slant height (l)

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

Ex.2: Another square pyramid Find the area of a square pyramid w/ base edges 10ft long & a slant height 13ft. V = (⅓)Bh = (⅓) 100•h = (⅓)100•___ = (⅓)1200 = 400ft3 a2 + b2 = c2 h2 + 52 = 132 h2 = 144 h = 12 13ft 12 h 5ft 10ft

Vc = ⅓Bh II. Volume of a Cone Cone – Is “pointed” like a pyramid, but its base is a circle. h Vc = ⅓Bh r Area of the Base A = r2  

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

Ex.4: Volume of a Composite Figure   Volume of Cylinder NEXT! V = Bh = r2h = (8)2(4) = 256 10cm 4cm   8cm

Ex.5: Solve for the missing variable. The following cone has a volume of 110. What is its radius. V = ⅓Bh V = ⅓(r2)h 110 = (⅓)r2(10) 110 = (⅓)r2(10) 11 = (⅓)r2 33 = r2 r = √33 cm 10cm r

Vc = ⅓Bh What have we learned??? Volume of Cones & Pyramids Height is the actual height of the solid not the slant height!!! Volume of Cones & Pyramids Vc = ⅓Bh h Area of Base h r