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:
[tex]V_{prism}=Bh[/tex]
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:
[tex]\begin{gathered} A_{righttriangle}=\frac{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=\frac{4in(3in)}{2}=\frac{12in^2}{2}=6in^2 \\ \\ A_t=B=6in^2 \\ \end{gathered}[/tex]
Then the base area is 6 square inches.
3. Now, we can determine the prism volume as follows:
[tex]\begin{gathered} V_{prism}=Bh=6in^2(8in)=48in^3 \\ \\ V_{prism}=48in^3 \end{gathered}[/tex]
Therefore, in summary, the prism volume is 48 cubic inches (option D.)
