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7-104.

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. Homework Help ✎

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

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:

$V=\sum_{i=0}^{15}\Delta xf(a+\Delta xi)$

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

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

2. Calculate the volume of this cake.

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