Question

A prism and pyramid have congruent triangular basis if their heights are both 15 m^3 what is the volume of each shape

The volume of the prism is
The volume of the pyramid is 280 m^3

Answer 1

[AI-generated answer — Bot GPT 3.5]

Volume of the prism = base area x height

Volume of the prism = (1/2 x base x height) x height
Volume of the prism = (1/2 x base x 15) x 15
Volume of the prism = 7.5 x base x 15
Since the volume of the prism is equal to 280 m^3, we can set up the equation 280 = 7.5 x base x 15 and solve for base:

280 = 112.5 x base
base = 280 / 112.5
base = 2.488 m

Therefore, the volume of the prism is:
Volume of the prism = (1/2 x 2.488 x 15) x 15
Volume of the prism = 186.75 m^3

Volume of the pyramid = (1/3 x base x height) x height
Volume of the pyramid = (1/3 x 2.488 x 15) x 15
Volume of the pyramid = (7.464 x 15) x 15
Volume of the pyramid = 111.96 x 15
Volume of the pyramid = 1679.4 m^3

Therefore, the volume of the pyramid is 1679.4 m^3.