Question

Relationship Between Volume of Prisms & Pyramids Practice%0D%0AComplete this assessment to review what you've learned. It will not count toward your grade.%0D%0A4 of 54 of 5 Items%0D%0A%0D%0AQuestion%0D%0AUse the image to answer the question.%0D%0A%0D%0A%0D%0A%0D%0AA prism and pyramid have congruent triangular bases. If their heights are both 15 m, what is the volume of each shape?%0D%0A%0D%0A(1 point)%0D%0AThe volume of the prism is m3. %0D%0AThe volume of the pyramid is m3.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the volume of each shape, we need to calculate the area of the triangular base and then multiply by the height.

The formula for the volume of a prism is V = Bh, where B is the area of the base and h is the height.

The formula for the volume of a pyramid is V = 1/3 Bh, where B is the area of the base and h is the height.

Since the base of the prism and pyramid are congruent triangles, we only need to calculate the area of one triangle.

Let's first calculate the area of the triangular base:
Area = 1/2 * base * height
Area = 1/2 * 10m * 6m
Area = 30 m^2

Now, let's calculate the volume of the prism:
V_prism = 30m^2 * 15m
V_prism = 450 m^3

Now, let's calculate the volume of the pyramid:
V_pyramid = 1/3 * 30m^2 * 15m
V_pyramid = 150 m^3

Therefore, the volume of the prism is 450 m^3 and the volume of the pyramid is 150 m^3.