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Consider a wedding cake of infinite height, each layer of which is a right circular cylinder of

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Consider a wedding cake of infinite height, each layer of which is a right circular cylinder of height 1. The bottom layer of the cake has a radius of 1, the second layer has a radius of 1/2, the third layer has a radius of 1/3, and the nth layer has a radius of 1/n (see figure). 

a. To determine how much frosting is needed to cover the cake, find the area of the lateral (vertical) sides of the wedding cake. What is the area of the horizontal surfaces of the cake?

b. Determine the volume of the cake.

c. Comment on your answers to parts (a) and (b).

Consider a wedding cake of infinite height, each layer of

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a The circumference of the kth layer is 2 so its area is 2 and thus the total vertical surfac...View the full answer


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Calculus Early Transcendentals

Calculus Early Transcendentals

ISBN: 978-0321947345

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Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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