1 / 16

13.1 Volumes of Prisms and Cylinders

13.1 Volumes of Prisms and Cylinders. 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. . Volumes of Prisms.

lieu
Télécharger la présentation

13.1 Volumes 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. 13.1 Volumes of Prisms and Cylinders

  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.

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

  5. Example 1: Volume of a Triangular Prism Find the volume of the right triangular prism. Use the Pythagorean Theorem to find the length of the base of the prism. 24 *Note: Remember, you can only use P.T. on Right Triangles! 15 20 a

  6. Example 1: Volume of a Triangular Prism Using Pythagorean Theorem to find the length of the base of the prism we get... a² + b² = c²  Pythagorean Theorem a² + 15² = 24² 24 a² + 225 = 576 a² = 351 15 a = √351 20 a ≈ 18.7 a

  7. Example 1: Volume of a Triangular Prism V = Bh  Volume of a Prism 24 B = ½(18.7)(15) h = 20 So… V =½(18.7)(15)(20) 15 20 V = 2,805 cubic centimeters 18.7

  8. Example 2: Volume of a Rectangular Prism Find the volume in feet of the rectangular prism. First, we must convert inches to feet. 10 ft 12 inches = 1 foot 12 in. 25 ft.

  9. Example 2: Volume of a Rectangular Prism Now, we can find the volume in feet of the rectangular prism. 1 ft. x 10 ft. x 25 = 250 ft. 10 ft. 1 ft. 25 ft.

  10. Volumes of Cylinders If a cylinder has a volume of V cubic units, a height of h units, and the bases have radii of r units, then V = Bh or V = πr²h h Area of Base =πr² r

  11. Example 3: Volume of a Cylinder Find the volume of each cylinder. The height h is 9.4 meters, and the radius r is 1.6 meters. V = πr²h 9.4m = π(1.6²)(9.4) ≈ 75.6 meters 1.6m

  12. Example 4: Volume of a Cylinder Find the volume of each cylinder. a² +b² = c²  Pythagorean Theorem h² + 7² = 15² h² + 49 = 225 h² = 176 7 in. 15 in. h ≈ 13.3 The diameter of the base, the diagonal, and the lateral edge of the cylinder form a right triangle. Use the Pythagorean Theorem to find the height.

  13. Example 4: Volume of a Cylinder Find the volume of each cylinder. V = π(3.5²)(13.3) V = 511.8 7 in. 13.3 in. The volume is approximately 511.8 cubic inches.

  14. 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. • Which basically means, that whether it is right or oblique, it’s volume is V=Bh

  15. Example 5: Volume of an Oblique Cylinder Find the volume of the oblique cylinder. 8 yd To find the volume, use the formula for a right cylinder. 13 yd V = πr²h = π(8²)(13) = 2,613.8 The volume is approximately 2,613.8 cubic yards.

  16. Assignment • Page 692 #7-24, 26

More Related