Question

The volume of this triangular prism is 1,001 cubic inches. What is the value of v?

v
14 in
11 in

v =
inches

Answer 1

To find the value of \( v \) for the triangular prism, we need to use the formula for the volume of a triangular prism, which is given by:

\[
V = \text{Base Area} \times \text{Height}
\]

The base area of the triangle can be calculated using the formula for the area of a triangle:

\[
\text{Base Area} = \frac{1}{2} \times \text{Base} \times \text{Height of Triangle}
\]

If we denote \( B \) as the base and \( h_t \) as the height of the triangle, then the volume becomes:

\[
V = \frac{1}{2} \times B \times h_t \times h_p
\]

where \( h_p \) is the height (or length) of the prism.

In your example, we have:

- Volume \( V = 1,001 \) cubic inches
- One dimension \( h_p = v \)
- Another dimension is given as \( 14 \) inches for the base of the triangle
- The height of the triangle is given as \( 11 \) inches

Now, substituting the known values into the volume formula:

1. Calculate the base area of the triangular face:

\[
\text{Base Area} = \frac{1}{2} \times 14 \times 11 = \frac{154}{2} = 77 \text{ square inches}
\]

2. Then substitute the base area into the volume formula:

\[
1,001 = 77 \times v
\]

3. Now solve for \( v \):

\[
v = \frac{1,001}{77} = 13
\]

Thus, the value of \( v \) is:

\[
v = 13 \text{ inches}
\]