Question

The volume of this triangular prism is 200 cubic meters. What is the value of y?

10 m
y
8 m

y =
meters

Answer 1

To find the value of \( y \) in the triangular prism with a volume of 200 cubic meters, we can use the formula for the volume of a prism:

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

In the case of a triangular prism, the base area is the area of the triangular base, and the height is the length of the prism.

Given the dimensions:

- The base is a triangle with a height of \( y \) meters and a base length of 8 meters.
- The length (or height of the prism) is 10 meters.

First, we will find the area of the triangular base. The area \( A \) of a triangle is given by:

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

Substituting the base (8 m) and the height (\( y \)) into the formula:

\[
A = \frac{1}{2} \times 8 \times y = 4y
\]

Now, we can express the volume \( V \) of the prism in terms of \( y \):

\[
V = A \times \text{height of the prism} = (4y) \times 10 = 40y
\]

Setting this equal to the given volume (200 cubic meters):

\[
40y = 200
\]

To find \( y \), we divide both sides by 40:

\[
y = \frac{200}{40} = 5
\]

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

\[
y = 5 \text{ meters}
\]