A gift shop sells a paperweight that is in the shape of a triangular prism. The diagram shows the dimensions of the paperweight.
Note: Figure is not drawn to scale.
If the volume of the paperweight is 96 cubic inches, what is the height of the triangular base of the paperweight?
To find the height of the triangular base of the paperweight, we first need to find the area of the triangular base using the formula for the volume of a triangular prism:
Volume = Base area x Height
Since the volume is 96 cubic inches and the base is a triangle (1/2 x base x height), we have:
96 = 1/2 x base x height x height
Simplifying, we get:
192 = base x height^2
We know the base is 8 inches (given in the diagram), so we can plug this in:
192 = 8 x height^2
Solving for height:
height^2 = 192 / 8
height^2 = 24
height = sqrt(24)
height ≈ 4.9 inches
Therefore, the height of the triangular base of the paperweight is approximately 4.9 inches.