Question

What is the volume of the following prism?A prism which has a right triangle for the base and a height of 8 inches. The legs of the right triangle are 4 inches and 3 inches.A. 108 in³B. 480 in³C. 96 in³D. 48 in³

Answer 1

We have the following prism:

• The prism has a right triangle for the base

,

• The height of the prism, h, is 8 inches (h = 8 inches)

,

• The legs of the right triangle are 4 inches, and 3 inches

And we have to determine the volume of the prism.

To find the volume of the prism we can proceed as follows:

1. We know that the general formula for calculating the volume of a prism is:

`V_(prism)=Bh`

Where:

• B is the base area

,

• h is the height of the prism

2. Therefore, we need to find the base area, and we know that the base is the right triangle given above. Then the area is:

`\begin{gathered} A_(righttriangle)=(ab)/(2) \\ \\ a\text{ is a leg of the triangle} \\ \\ b\text{ is the other leg of the triangle} \\ \\ a=4in,b=3in \\ \\ \text{ Therefore:} \\ \\ A_t=(4in(3in))/(2)=(12in^2)/(2)=6in^2 \\ \\ A_t=B=6in^2 \\ \end{gathered}`

Then the base area is 6 square inches.

3. Now, we can determine the prism volume as follows:

`\begin{gathered} V_(prism)=Bh=6in^2(8in)=48in^3 \\ \\ V_(prism)=48in^3 \end{gathered}`

Therefore, in summary, the prism volume is 48 cubic inches (option D.)