Question

This prism has a right triangle for a base. What is the volume of the prism?

Answer 1

The volume of a prism with a right triangle base is determined by finding the area of the base using the formula (1/2 × base × height) and then multiplying by the height of the prism.

Step-by-step explanation:

The volume of a prism with a right triangle base can be calculated using the formula V = (1/2 × base x height) of the triangle × length of the prism. Since we know the general formula for the volume of a prism is V = Ah, where A is the area of the base and h is the height (or length) of the prism. For a right triangular base, the area would be calculated as 1/2 × base × height of the triangle. Once the area is found, multiply that by the height of the prism to get the volume.

Answer 2

length = 6 x 1/3 = 2 inches

width = 4 x 1/3 = 4/3 inches

height = 8 x 1/3 = 8/3 inches

volume = lwh = 2 x 4/3 x 8/3 = 64/9 cubic inches

Another approach is the following:

There are 6 x 4 x 8 = 192 cubes inside the prism,.

Each cube has a volume of 1/27 cubic inches.

Therefore total volume = 192 x 1/27 = 192/27 = 64/9