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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. Volume. Volume – Is the space that a figure occupies. Measured in cubic units. cm 3 , in 3 , m 3 , ft 3. I. Finding the volume of a Prism.

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Volumes of Prisms & Cylinders

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

  2. Volume Volume – Is the space that a figure occupies. Measured in cubic units. cm3, in3, m3, ft3

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

  4. 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? Ex. 1: Finding the Volume of a rectangular prism

  5. Ex.1: Find the Volume of the Prism Area of Base B = l•w V = Bh = (3in • 5in)(10in) = (15in2)(10in) = 150in3 10in 3in 5in

  6. Ex.2: Find the volume of the following Triangle 29m V = Bh = ½bh • h = ½(20m)__ • (40m) = 210m2 • 40m = 8400m3 a 40m 21 20m Height of the base: a2 + b2 = c2 a2 + 202 = 292 b = 21

  7. Ex.3: Yet another prism! Find the volume. h = 6.9 10in V = Bh = ½bh • h = ½(8in) __ • (10in) = (27.7in2) • (10in) = 277in3 8in 6.9

  8. II. Volume of a Cylinder Height of cylinder r V = Bh h Volume of right cylinder Area of base: (Circle) A = r2

  9. Ex.4: Find the area of the following right cylinder. Area of a Circle V = Bh = r2• h = (8ft)2 • (9ft) = 64ft2 • (9ft) = 576ft3 = 1809.6ft3 16ft 9ft

  10. Ex.5: Find the volume of the following composite figure. Half of a cylinder: Vc = Bh = r2•h = (6in)2 • (4in) = 452in3 = 452/2 = 226in3 11in 4in Volume of Prism: Vp = Bh = (11)(12)(4) = 528in3 12in VT = Vc + Vp = 226in3 + 528in3 = 754in3

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