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

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

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

    represents the height of each cylindrical layer of cake.

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

  2. Calculate the volume of this cake.

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