Question

A wedge of cheese is shaped like a triangular prism. The wedge of cheese is 7 inches tall. The base of the cheese is shaped like a triangle with a base of 11 and a height of 5 inches. If you ate this whole block of cheese, about how many cubic inches would you have eaten (ignoring the holes)?

420 in
193 in
385 in
210 in

Answer 1

193 in

Explanation:

Volume of a triangular prism:

The volume of a triangular prism is the base area multiplied by the wedge, that is:

`V = A_bw`

The base area is one half times the triangle base times it's height, so:

`V = 0.5*b*h*w`

The wedge of cheese is 7 inches tall.

This means that
`w = 7`

The base of the cheese is shaped like a triangle with a base of 11 and a height of 5 inches.

This means that
`b = 11, h = 5`

Volume:

`V = 0.5*b*h*w = 0.5*11*5*7 = 192.5`

Rounding, approximately 193 in.