the base of a rectangular prism is congruent to the base of a pyramid. The height of the pyramid is 3 times the height of the prism. Which figure has a greater volume? Explain.
I'm terrible with these kind of word problems. If you could explain that would be great.
let height of prism be h
let height of pyramid be 3 h, (they said so.)
volume of prism = (base)(h)
volume of pyramid = (1/3)(base)(3h)
= (base)(h)
They are the same !
ooohhhhh! I get it now! thanks so much!
The volume of the rectangular prism
= base area x height
the volume of the pyramid
= (1/3) base x height
If the height of the pyramid is 3 times the height
the factor of 3 would cancel the 1/3 of the formula, and their volumes would be equal.
wai the height of the pyramid is 3 times the height?
Can you just show how you got it with numbers like how you would on a piece of paper. Thanks!
To determine which figure has a greater volume, we need to first understand the formulas for finding the volume of each figure.
The volume of a rectangular prism is given by the formula: V_prism = length * width * height.
The volume of a pyramid is given by the formula: V_pyramid = (1/3) * base_area * height.
Since the base of the rectangular prism is congruent to the base of the pyramid, we can assume that they have the same length and width. Let's call these dimensions x.
Now, let's consider the height of each figure. Given that the height of the pyramid is 3 times the height of the prism, let's call the height of the prism h. Therefore, the height of the pyramid would be 3h.
Now, we can calculate the volumes of each figure using their respective formulas:
Volume of the prism: V_prism = x * x * h = x^2 * h.
Volume of the pyramid: V_pyramid = (1/3) * x * x * 3h = (x^2 * h).
Comparing the two volumes, we can see that they are equal: V_prism = V_pyramid = x^2 * h.
Therefore, since the volumes of the prism and the pyramid are identical, they have the same volume. The answer is that both figures have the same volume.