Use the image to answer the question a prism and pyramid have congruent triangular bases if their heights are both 15 M what is the volume of each shape

Answer 1

To calculate the volume of a prism, you use the formula V = B * h, where B is the area of the base and h is the height.

In this case, the base of the prism is a triangle, so the area of the base is (1/2)*b*h, where b is the base length of the triangle. Since the base of the prism and pyramid are congruent triangles, the base length of the prism is the same as the base length of the pyramid.

Therefore, the volume of the prism is:

V_prism = (1/2)*b*h * h = (1/2)*b*h^2 = (1/2)*b*15^2 = (1/2)*b*225

To calculate the volume of the pyramid, you use the formula V = (1/3)*B*h, where B is the area of the base and h is the height.

Again, the base of the pyramid is a triangle, so the area of the base is (1/2)*b*h. Therefore, the volume of the pyramid is:

V_pyramid = (1/3)*(1/2)*b*h * h = (1/6)*b*h^2 = (1/6)*b*15^2 = (1/6)*b*225

So, the volume of the prism is (1/2)*b*225 cubic units and the volume of the pyramid is (1/6)*b*225 cubic units.