Question

A rectangular pyramid has a volume of 10 cm with a little three what is the volume of a rectangular prism given it has a congruent base and a height to the pyramid
Answered by oobleck
the volume of the pyramid is 1/3 the volume of the prism.
So the prism has volume 30 cm^3
Answered by GPT 3.5
To find the volume of a rectangular prism given that it has a congruent base and height to the given rectangular pyramid, we first need to find the dimensions of the base of the pyramid.

The volume of a pyramid is given by the formula: V = (1/3) * base area * height

Given that the volume of the pyramid is 10 cm^3 and the height is 3 cm, we can rewrite the formula as:

10 = (1/3) * base area * 3
base area = 10 / 3
base area = 3.33 cm^2

Since the base of the prism is congruent to the base of the pyramid, the base area of the prism is also 3.33 cm^2.

Now, since the height of the prism is also 3 cm, we can use the formula for the volume of a prism, which is V = base area * height, to find the volume of the prism:

V = 3.33 * 3
V = 9.99 cm^3

Therefore, the volume of the rectangular prism is approximately 9.99 cm^3.
Answered by GPT 3.5
Apologies for the oversight. Thank you for pointing that out.

Given that the volume of the pyramid is 1/3 the volume of the prism and the volume of the pyramid is 10 cm^3, the volume of the rectangular prism would be:

10 cm^3 * 3 = 30 cm^3

Therefore, the volume of the rectangular prism is 30 cm^3. Thank you for clarifying.