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13.1 Volumes of Prisms and Cylinders

13.1 Volumes of Prisms and Cylinders. By: Shelbi Legg and Taylor Mastin. Objectives. Find volumes of prisms. Find volumes of cylinders. Volumes of Prisms. The volume of a figure is the measure of the amount of space that a figure encloses. Volume is measured in cubic units. (units³)

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13.1 Volumes of Prisms and Cylinders

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  1. 13.1 Volumes of Prisms and Cylinders By: Shelbi Legg and Taylor Mastin

  2. Objectives • Find volumes of prisms. • Find volumes of cylinders.

  3. Volumes of Prisms • The volume of a figure is the measure of the amount of space that a figure encloses. • Volume is measured in cubic units. (units³) • You can create a rectangular prism from different views of the figure to investigate its volume.

  4. Volumes of Prisms • If a prism has a volume of Vcubic units, a height of h units, and each base has an area of B square units, then V=Bh. h Area of Base=B

  5. Example 1: Volume of a Triangular Prism Find the volume of the triangular prism. 17 cm 8 cm 13 cm a

  6. Example 1 cont… • a² + b² = c² Use Pythagoream Theorem. • a² + 8² = 17² b=8, c=17 • a² + 64 = 289 Multiply. • a² = 225 Subtract 64 from both sides. • a = 15 Take the square root of both sides. • V= Bh Next, find the volume of the prism. • V=½(8)(15)(13) Substitute the numbers in. • V=780 cm³ Multiply.

  7. Example 2: Volume of a Rectangular Prism Find the volume of the rectangular prism.

  8. Example 2 cont… • 8(3)= 24 Find the area of the base. • V= 24(12) Then plug the area of the base into the formula. • V= 288 in³ Multiply.

  9. Volume of Cylinder • If a cylinder has a volume of V cubic units, a height of h units, and the bases have radii of runits, then V=Bhor V=πr²h. r Area of base= πr²

  10. Example 1: volume of a cylinder • Find the volume of the cylinder. h=12.4 r= 4.6 m

  11. Example 1 cont… • V= ¶r²h Use the volume formula for cylinders. • V= ¶(4.6²)(12.4) r= 4.6 m, h= 12.4 m • V≈824.3 m³ Multiply. 12.4 R= 4.6

  12. 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.

  13. Oblique Cylinders • If a cylinder has a base with an area of B square units and a height of h units, then its volume is Bh cubic units, whether it is right or oblique. h

  14. Example 1: Volume of an Oblique Cylinder • Find the volume of the oblique cylinder. 4 yd 9 yd

  15. Example 1 cont… • V= ¶r²h Use the formula for a right cylinder. • V=¶(4²)(9) r=4 yd, h=9 yd • V= 452.4 yd³ 4 9

  16. Assignment Pg. 692 #7-24

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