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Sec. 11 – 4 Volumes of Prisms & Cylinders Objectives: 1) To find the volume of a prism. 2) To find the volume of a cylinder.

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Volume ►V►V►V►Volume – Is the space that a figure occupies. MMMMeasured in cubic units. ►c►c►c►cm3, in3, m3, ft3 ►T►T►T►Th(10-5) Cavalieri’s Principle IIIIf 2 space figures have the same height & the same cross-sectional area @ every level, then they have the same volume.

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I. Finding the volume of a Prism ► Prism – 2 parallel bases, sides (Lats) are rectangles. Height (h) Area of Base (B) V = Bh Height of Prism Area of Base A = bh (Rectangle) A = ½bh (Triangle) A = ½ap (Polygon)

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Ex. 1: Finding the Volume of a rectangular prism ► The box shown is 5 units long, 3 units wide, and 4 units high. How many unit cubes will fit in the box? What is the volume of the box?

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Ex.1: Find the Volume of the Prism 5in 3in 10in V = Bh = (3in 5in)(10in) = (15in 2 )(10in) = 150in 3 Area of Base B = lw

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Ex.2: Find the volume of the following 20m 29m 40m V = Bh = ½bh h = ½(20m)__ (40m) = 210m 2 40m = 8400m 3 Height of the base: a a 2 + b 2 = c 2 a 2 + 20 2 = 29 2 b = 21 Triangle 21

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Ex.3: Yet another prism! Find the volume. 8in 10in V = Bh = ½bh h = ½(8in) __ (10in) = (27.7in 2 ) (10in) = 277in 3 4 8 h 60° Sin 60 = h/8.866 = h/8 6.9 = h 6.9

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Cavalieri’s Principle If two solids have the same height and the same cross-sectional area at every level, then they have the same volume.

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II. Volume of a Cylinder r h V = Bh Volume of right cylinder Height of cylinder Area of base: (Circle) A = r 2

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Ex.4: Find the area of the following right cylinder. 16ft 9ft V = Bh = r 2 h = (8ft) 2 (9ft) = 64 ft 2 (9ft) = 576 ft 3 = 1809.6ft 3 Area of a Circle

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Ex.5: Find the volume of the following composite figure. Half of a cylinder: V c = Bh = r 2 h = (6in) 2 (4in) = 452in 3 = 452/2 = 226in 3 12in 4in 11in Volume of Prism: V p = Bh = (11)(12)(4) = 528in 3 V T = V c + V p = 226in 3 + 528in 3 = 754in 3

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What have we learned?? Volume of a prism or a cylinder: V = Bh Capitol “B” stands for area of the base. Composite Figures: Made up of two separate solids.

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