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.
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?
1 answer
1 answer