1 / 12

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

yaakov
Download Presentation

Lesson 13.1-Volume of Prisms and Cylinders

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related