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7-22.

THE WEDDING CAKE, Part One

Kiki is ordering a wedding cake for her upcoming reception. She is considering a four-layer circular cake, where the diameters are $16$, $12$, $8$, and $4$ inches. Each layer will be $4$ inches tall. Homework Help ✎

1. Write a Riemann sum to approximate the volume of Kiki’s cake.

Recall that a Riemann sum is a sum of the area of many rectangles.
Sigma notation is a tool to concisely write that sum, but it is not essential that you use sigma notation.

2. The bakery has informed Kiki that she should have approximately $7$ in3 of cake per guest at the reception. She expects 200 guests at her wedding. Will she have enough cake?

In order for Kiki to have enough cake to feed her guests, the total volume of all 4 layers of cake should exceed 7(200) = 1400 cubic inches.