7. This shape will be used in both questions 7 and 8.
A prism and a pyramid have congruent triangular bases. If their heights are both 15 m, what is the volume of the PRISM?
(1 point)
To find the volume of a prism, you need to multiply the area of the base by the height. Since the base of the prism is a congruent triangle to the pyramid, the area of the base will be the same as the area of the triangular base of the pyramid.
First, calculate the area of the triangle base.
Area = 1/2 * base * height
Since we know the height is 15 m, we need to find the base of the triangle.
Since the triangles are congruent, the base of the prism is the same as the base of the pyramid. Let's call it base = b.
Using the Pythagorean Theorem (a^2 + b^2 = c^2), we know that:
(5)^2 + b^2 = (10)^2
25 + b^2 = 100
b^2 = 100 - 25
b^2 = 75
b = √75 = 5√3
Now we can find the area of the base of the prism:
Area = 1/2 * base * height
Area = 1/2 * 5√3 * 15
Area = 37.5√3 m^2
Now, calculate the volume of the prism:
Volume = area of base * height
Volume = 37.5√3 m^2 * 15 m
Volume ≈ 843.75 m^3
Therefore, the volume of the prism is approximately 843.75 cubic meters.