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Lesson 13.1-Volume of Prisms and Cylinders

Lesson 13.1-Volume of Prisms and Cylinders. Objectives. Find volumes of prisms Find volumes of cylinders. Definition of Volume. Volume is a measure of the amount of space that a figure encloses Volume is always recorded in cubic units ex. cm. 3

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Lesson 13.1-Volume of Prisms and Cylinders

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  1. Lesson 13.1-Volume of Prisms and Cylinders

  2. Objectives Find volumes of prisms Find volumes of cylinders

  3. Definition of Volume Volume is a measure of the amount of space that a figure encloses Volume is always recorded in cubic units ex. cm.3 Remember that if there is a part cut out of the center of the figure you have to subtract it’s volume from the volume of the entire figure

  4. Base Height • To find the volume of a prism use the formula V=Bh V=Volume B=Area of the base h=height of prism

  5. Example #1 Find the volume of this figure 10ft. 12 ft. 13ft.

  6. 10ft. 12ft. 13ft. 13ft. x 5ft. 1)Find the area of the triangular base 2)Create the height of one of the bases and use Pythagorean Theorem to find the height of the base. 3)132=52+x2 4) x2= 144 5) h= 12 6)Find area of triangular base, A=1/2(10)(12) A=(5)(12) A=60ft.2 7)V=Bh V=(60)(12) V=720ft.3

  7. Volume of Cylinders To find the volume of a cylinder, use V=πr²h This is basically the area of height of the base times the height just like in a prism radius

  8. Example #2 24m. 1)Take ½ of the diameter to get the radius. 2)1/2 of the diameter is twelve, now plug everything into the formula 3)V= π(122)(30) 4) V=(144)(π)(30) 5)V=4320π or 13,571.7m.3 30m.

  9. Example #3 • Sometimes it gives you the diagonal of the cylinder and you have to use the Pythagorean Theorem to find the height. • 102 = 62+x2 • X2=64 • X=8ft. • Now plug everything into the formula • V=32π(8) • V=9π8 • V=72π or 226.2 ft.3 10 ft. 6 ft. x

  10. Cavalieri’s Principle 1) If two solids have the same height and the same cross-sectional area at every level, then they have the same volume…….

  11. Example #4 • Sometimes the cylinder is not a right cylinder and the height will be outside the cylinder. • Use the same formula using the height that is outside the cylinder. • V=42π(9) • V=16π(9) • V=144π or 452.4 yds.3 9 yd. 4 yd.

  12. Assignment P.692 #7-16, #18, #22-23 Bonus-#28

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