Question

The volume of this triangular prism is 935 cubic centimeters. What is the value of j?

11 cm
j
10 cm

j =
centimeters

Answer 1

To find the value of \( j \) in the triangular prism with a volume of 935 cubic centimeters, we can use the formula for the volume of a prism, which is given by:

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

For a triangular prism, the base area can be calculated using the formula for the area of a triangle:

\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]

In this case, the base of the triangular base of the prism is \( 10 \) cm, and its height is \( j \) cm. Therefore, the area of the triangle (base area of the prism) is:

\[
\text{Area} = \frac{1}{2} \times 10 \times j = 5j
\]

Now, if we consider \( h \) to be the height of the prism (which is \( 11 \) cm), we can rewrite the volume formula as:

\[
\text{Volume} = \text{Base Area} \times \text{Height} = 5j \times 11
\]

Setting this equal to the volume of the prism, we have:

\[
5j \times 11 = 935
\]

Calculating \( 5j \times 11 \):

\[
55j = 935
\]

Now, we can solve for \( j \):

\[
j = \frac{935}{55}
\]

Calculating \( \frac{935}{55} \):

\[
j = 17
\]

Therefore, the value of \( j \) is:

\[
\boxed{17 \text{ cm}}
\]