The lateral (side) surface area of a cone of height h and base radius r should be pai rsqrt(r2 + h2), the semiperimeter of the base times the slant height. Show that this is still the case by finding the area of the surface generated by revolving the line segment y = (r/h) x, 0<=x<= h, about the x-axis.

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter9: Surfaces And Solids
Section9.3: Cylinders And Cones
Problem 21E: The oblique circular cone has an altitude and a diameter of base that are each of length 6 cm. The...
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The lateral (side) surface area of a cone of height h and base radius r should be pai rsqrt(r2 + h2), the semiperimeter of the base times the slant height. Show that this is still the case by finding the area of the surface generated by revolving the line segment y = (r/h) x, 0<=x<= h, about the x-axis.

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