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Volumes of Prisms & Cylinders 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

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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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Finding the Volume of a Prism ► What is the volume of the rectangular prism?

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What is the volume of the rectangular prism?

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What is the volume of the triangular prism?

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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 volume 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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Finding the Volume of a Cylinder ► What is the volume of the cylinder in terms of π?

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What is the volume of the cylinder at the right in terms of π?

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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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11.4 Volumes of Prisms and Cylinders

11.4 Volumes of Prisms and Cylinders

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