Explanation Calculation: A right circular cone can be thought of as a solid of revolution of the curve y = − r h x + r for all. x ∈ [ 0 , h ] about the x -axis. This allows us to find the lateral surface area A , which is A = ∫ 0 h 2 π y 1 + [ f ' ( x ) ] 2 d x = 2 π ∫ 0 h ( − r h x + r ) 1 + ( − r h ) 2 d x

6th Edition

ISBN: 9781465208880

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Cylinders

A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.

Cones

A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is dr…

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Chapter 6, Problem 41SP

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To Find:Surface area of a right circular cone with (top) radius r and height h .

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Chapter 6, Problem 40SP

Chapter 6, Problem 42SP

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Chapter 6 Solutions

Calculus

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Surface area of a right circular cone with (top) radius r and height h .

Solution Summary: The author calculates the lateral surface area of a right circular cone with (top) radius r and height h.

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Chapter 6 Solutions