THE WEDDING CAKE, Part Three

Kiki is still trying to decide the shape of her wedding cake. She is now considering having $16$ layers! The largest diameter would be $16$ inches and each subsequent diameter would decrease by $1$ inch. Each layer of this cake would only be $1$ inch tall.

1. Setup a Riemann sum to calculate the volume of the cake.

   Hint 1(a):

   Since there are $16$ layers of cake, and $16$ is a large number, it would be beneficial to write the Riemann sum in sigma notation:

   Hint 2(a):

   $Δx$ represents the height of each cylindrical layer of cake.

   Hint 3(a):

   Figure out the radius of the smallest layer. This will give you the initial value $a$.

2. Find the volume of this cake.

   Hint (b):

   No need to expand. Use a calculator to evaluate the sigma notation.