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. a. Write the volume of the cake as an infinite sum in expanded form and in sigma notation. b. Determine whether the volume converges or diverges by using the proper test c. Do some research to find the exact volume of the cake
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 drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.
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.
a. Write the volume of the cake as an infinite sum in expanded form and in sigma notation.
b. Determine whether the volume converges or diverges by using the proper test
c. Do some research to find the exact volume of the cake
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