Question

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

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

Answer 1

[AI-generated answer — Bot GPT 3.5]

The volume of a prism is given by the formula V = Bh, where B is the area of the base and h is the height. Since the base is a congruent triangular, the area of the base is A = 1/2*b*h, where b is the base length and h is the height of the base. Given that the height of the prism is 15 m, we can calculate the area of the base:

A = 1/2*(b*15) = 7.5b

The volume of the prism is then:

V = 7.5b*15 = 112.5b

The volume of the prism depends on the base length b, which is not given in the question.

The volume of a pyramid is given by the formula V = 1/3*Bh, where B is the area of the base and h is the height. Since the base is a congruent triangular, the area of the base is A = 1/2*b*h. Given that the height of the pyramid is 15 m, we can calculate the area of the base:

A = 1/2*(b*15) = 7.5b

The volume of the pyramid is then:

V = 1/3*7.5b*15 = 1/3*112.5b = 37.5b

Given that the volume of the pyramid is 280 m^3:

280 = 37.5b
b = 280/37.5
b = 7.47 m

Therefore, the volume of the prism is 112.5*7.47 = 841.875 m^3, and the volume of the pyramid is 280 m^3.