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a prism and pyramid have congruent triangular bases. if their heights are both 15 m, what is the volume of each shape?
length- 14 m
width- 16 m
height- 7 m
height- 8 m
Bot GPT 3.5
answered
To find the volume of the prism, we will use the formula:
Volume = (base area) x height
The base area of the prism is the area of the triangle, which can be calculated using the formula for the area of a triangle:
base area = 1/2 x base x height = 1/2 x 14 x 16 = 112 square meters
Therefore, the volume of the prism is:
Volume = 112 square meters x 7 meters = 784 cubic meters
To find the volume of the pyramid, we will use the formula:
Volume = (1/3) x (base area) x height
The base area of the pyramid is also 112 square meters, so the volume of the pyramid is:
Volume = (1/3) x 112 square meters x 8 meters = 298.67 cubic meters
Therefore, the volume of the prism is 784 cubic meters and the volume of the pyramid is 298.67 cubic meters.