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?

8 feet cubed

12 feet cubed

36 feet cubed

38 feet cubed

Answer 1

12

Explanation:

Answer 2

The space inside the empty hood is option 2. 12 feet cubed.

Explanation:

Step 1:

To determine the space inside the hood, we need to determine the volume of the triangular prism.

To determine the volume of the prism, we multiply the height of the prism with the area of the base.

The base of the prism is a triangle and the area of a triangle is half the product of its base length and its height.

The area of a triangle
`= (1)/(2) (b)(h).`

Step 2:

The triangle has a base length of 3 feet and a height of 2 feet.

So the area of a triangle
`= (1)/(2) (b)(h) = (1)/(2) (3)(2)= 3` square feet.

The volume of the prism = (The area of the base)(height).

The height of the prism is 4 feet and the area of the base is 3 square feet.

The volume of the prism
`= 3(4) = 12` cubic feet = 12 ft³.

The volume of the prism is 12 feet cubed which is option 2.