A prism and pyramid have congruent triangular bases. If their heights are both 15 m, what is the volume of each shape?
(1 point)
The volume of the prism is m ^ 3
The volume of the pyramid is m ^ 3
To find the volume of each shape, we need to know the area of the triangular base first. Let's assume that the base of both the prism and pyramid is an equilateral triangle.
The formula for the area of an equilateral triangle is:
Area = (sqrt(3) / 4) * side length^2
Since the base of the prism and pyramid are congruent, the base area of both shapes will be the same.
Now, let's calculate the base area of the equilateral triangle:
Area = (sqrt(3) / 4) * 15^2
Area = (sqrt(3) / 4) * 225
Area = (sqrt(3) / 4) * 225
Area = sqrt(3) * 56.25
Area = 97.43 m^2 (approx)
Now, we can calculate the volume of the prism and pyramid with the given height of 15 m:
Volume of Prism = Base Area * Height
Volume of Prism = 97.43 * 15
Volume of Prism = 1461.45 m^3 (approx)
Volume of Pyramid = (1/3) * Base Area * Height
Volume of Pyramid = (1/3) * 97.43 * 15
Volume of Pyramid = 487.79 m^3 (approx)
Therefore, the volume of the prism is approximately 1461.45 m^3 and the volume of the pyramid is approximately 487.79 m^3.