THE WEDDING CAKE, Part One

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

1. Write a Riemann sum to approximate the volume of her cake.

   Hint (a):

   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 her that she should intend to have approximately $7$ in^{$^{3}$} of cake per guest at the reception. She expects $200$ guests at her wedding. Will she have enough cake?

   Hint (b):

   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.