Question

The hood above the stove in a restaurant kitchen is filled with fans and other ventilation parts.

A triangular prism. The triangular sides have a base of 3 feet and height of 2 feet. The prism has a height of 4 feet.

How much space is there inside the empty hood?

Answer 1

To find the volume of the triangular prism representing the hood above the stove, we can use the formula for the volume of a prism:

\[
V = B \times h
\]

where \(B\) is the area of the base of the prism and \(h\) is the height of the prism.

1. **Calculate the area of the triangular base**:

The area \(A\) of a triangle can be calculated using the formula:

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

For the triangular base with a base of 3 feet and height of 2 feet:

\[
A = \frac{1}{2} \times 3 \, \text{ft} \times 2 \, \text{ft} = \frac{1}{2} \times 6 \, \text{ft}^2 = 3 \, \text{ft}^2
\]

2. **Calculate the volume of the prism**:

The prism has a height of 4 feet, so we can substitute \(B\) and \(h\) into the volume formula:

\[
V = B \times h = 3 \, \text{ft}^2 \times 4 \, \text{ft} = 12 \, \text{ft}^3
\]

Thus, the space inside the empty hood is:

\[
\boxed{12 \, \text{ft}^3}
\]