8.2 - 8.2 Area of a Surface of Revolution(Dated November 8...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 8.2: Area of a Surface of Revolution (Dated: November 8, 2011) THE SURFACE AREA OF A FRUSTUM OF A CIRCULAR CONE Consider a circular cone with base radius r and slant height l . It can be flattened to form a sector of a circle with radius l and central angle θ = 2 π r 2 π l · 2 π = 2 π r l . It follows that the surface area of the cone is given by A = θ 2 π · π l 2 = π rl . Consider instead the frustum of a cone with slant height l and upper and lower radii r 1 and r 2 respectively. If the slant height of the cone is l 1 + l , then the surface area of the frus- tum is given by A = π r 2 ( l 1 + l )- π r 1 l 1 = π [( r 2- r 1 ) l 1 + r 2 l ]. On the other hand, from similar triangles one has l 1 r 1 = l 1 + l r 2 , from which it follows that ( r 2- r 1 ) l 1 = r 1 l . Hence the area of the frustum is also given by A = π ( r 1 + r 1 ) l = 2 π rl , where r = r 1 + r 2 2 is the average radius of the frustum. THE AREA OF A SURFACE OF REVOLUTION A surface of revolution can be obtained by rotating a curve y = f ( x ), a ≤ x ≤ b , about the x-axis, where f is positive and smooth. To calculate the area S of the sur-...
View Full Document

This note was uploaded on 11/11/2011 for the course MATH 152.01 taught by Professor Geline during the Fall '09 term at Ohio State.

Page1 / 2

8.2 - 8.2 Area of a Surface of Revolution(Dated November 8...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online