Question

A cake has two layers. Each layer is a regular hexagonal prism. You cut and remove a slice that takes away one face of each prism as shown. What is the volume of the​ slice? What is the volume of the remaining​ cake?

Answer 1

The volume of the slice is 129 in^3 and that of the remaining cake is 374. 4 in^3

How to determine the volume

Using the formula:

Volume = 3abh

Where a = apothem length

b = length of the side of the base

h =height of the prism

Substitute values from the diagram into the formula

Volume = 3 × 5 × 4.3 × 2

Volume = 129 in^3

Volume of the remaining cake

Volume = 3abh

Volume = 3× 5.2 × 4 × 6

Volume = 374. 4 in^3

Thus, the volume of the slice is 129 in^3 and that of the remaining cake is 374. 4 in^3

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