The volume of a triangular prism three times larger than a congruent pyramid
To find the volume of a triangular prism three times larger than a congruent pyramid, we need to first determine the volume of the congruent pyramid.
The volume of a pyramid is given by the formula:
V = (1/3) * B * h
where:
V = volume of the pyramid
B = area of the base of the pyramid
h = height of the pyramid
Since the pyramid is congruent to the prism, the base of the pyramid is the same as the base of the prism.
Let's say the volume of the congruent pyramid is V_p.
Now, if the volume of the triangular prism is three times larger than the volume of the congruent pyramid, we can write:
V_prism = 3 * V_p
Let's denote the volume of the triangular prism as V_prism.
Since the prism is a triangular prism, the volume of the prism can be calculated using the formula:
V_prism = B * h_prism,
where:
B = area of the base of the prism,
h_prism = height of the prism.
Since the prism is three times larger than the congruent pyramid:
V_prism = 3 * V_p = B * h_prism.
Thus, the volume of the triangular prism three times larger than a congruent pyramid is three times the volume of the congruent pyramid, and both have the same base area but different heights.