Download presentation

Presentation is loading. Please wait.

Published byCayden Tonks Modified over 9 years ago

1
Section 8.3 Nack/Jones1 8.3 Cylinders & Cones

2
Section 8.3 Nack/Jones2 Cylinders A cylinder has 2 bases that are congruent circles lying on parallel planes. The cylinder is a right cylinder if the line joining the centers of the circles called an axis is an altitude—that is, perpendicular to the planes of the circular bases.

3
Section 8.3 Nack/Jones3 Surface Area of a Cylinder Theorem 8.3.1: The lateral area L of a right circular cylinder with altitude of length h and circumference C of the base is given by: L = hC or L = 2 rh Theorem 8.3.2: The total area T of a right circular cylinder with base area B and lateral area L is given by: T = L + 2B or T = 2 rh + 2 r² Example: For the figure: L = 2 5 12 = 120 sq. units T = 120 + 2 5² = l70 sq. units. h = 12 5

4
Section 8.3 Nack/Jones4 Volume of a Cylinder Theorem 8.3.3: The volume V of a right circular cylinder with base area B and altitude of length h is given by: V = Bh or V = r²h Example: The volume of the right cylinder with radius = 5 and height = 12 is: V = 5² (12) = 60 units 3

5
Section 8.3 Nack/Jones5 Cone The solid figure formed by connecting a circle with a point not in the plane of the circle is called a cone. A cone has one base. Right cone: the altitude passes through the center of the base circle. Also the slant height is the distance l Oblique cone: If the altitude, h, is not perpendicular to the base.

6
Section 8.3 Nack/Jones6 Surface Area of a Cone Theorem 8.3.4: The lateral area L of a right circular cone with slant height of length l and circumference C of the base is given by: L = ½ l C or L = ½ l (2 r) Theorem 8.3.5: The total area T of a right circular cone with base area B and lateral area L is given by: T = B + L or T = r² + r l Theorem 8.3.6: In a right circular cone, the lengths of the radius r (of the base), the altitude h, and the slant height l satisfy the Pythagorean Theorem; that is l ² = r² + h² in every right circular cone.

7
Section 8.3 Nack/Jones7 Volume of a Cone Theorem 8.3.7: The volume V of a right circular cone with base area B and altitude of length h is given by: V = ⅓ Bh V = ⅓ r²h Solids of Revolution Locus of points when we rotate a plane region around a line segment which becomes the axis of the resulting solid formed. Figure 8.35 and Example 6 p. 415 - 6

8
Section 8.3 Nack/Jones8 Solids of Revolution P. 394-5 Practice exercises: p. 397, #24.

Similar presentations

© 2024 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google