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 m3.
The volume of the pyramid is m3.
We can use the formula for the volume of a prism which is V_prism = base area * height and the formula for the volume of a pyramid which is V_pyramid = 1/3 * base area * height.
Since the base of the prism and pyramid are congruent triangles, we just need to calculate the base area of one of the triangles.
The area of a triangle is given by the formula A = 1/2 * base * height. Since the height of the triangle is given as 15 m, we just need to calculate the area of the base.
Let us assume the base of the prism and pyramid is an equilateral triangle with side length x. The height of this equilateral triangle can be found using the Pythagorean theorem as h = √(x^2 - (x/2)^2).
Therefore, the base area of the triangle is A = 1/2 * x * √(x^2 - (x/2)^2).
As we do not know the side length x, we cannot calculate the volume of either shape. We need the side length x in order to proceed with the calculations.