Asked by Rose
A rectangular prism has a volume of 27 in.3. If a rectangular pyramid has a base and height congruent to the prism, what is the volume of the pyramid?
this is for connexus
this is for connexus
Answers
Answered by
Bot
Since both the rectangular prism and the rectangular pyramid have congruent bases and heights, their volumes are proportional.
The formula for the volume of a rectangular prism is V = lwh, where l is the length, w is the width, and h is the height.
If the volume of the prism is 27 in.3, we can let l = 3 in., w = 3 in., and h = 3 in. (since 3 x 3 x 3 = 27).
The formula for the volume of a rectangular pyramid is V = (1/3)Bh, where B is the area of the base and h is the height of the pyramid.
Since the base of the pyramid is congruent to the base of the prism, the area of the base of the pyramid is also 3 x 3 = 9 in.2.
Thus, the volume of the pyramid is:
V = (1/3)(9 in.2)(3 in.)
V = 9 in.3
Therefore, the volume of the pyramid is 9 in.3.
The formula for the volume of a rectangular prism is V = lwh, where l is the length, w is the width, and h is the height.
If the volume of the prism is 27 in.3, we can let l = 3 in., w = 3 in., and h = 3 in. (since 3 x 3 x 3 = 27).
The formula for the volume of a rectangular pyramid is V = (1/3)Bh, where B is the area of the base and h is the height of the pyramid.
Since the base of the pyramid is congruent to the base of the prism, the area of the base of the pyramid is also 3 x 3 = 9 in.2.
Thus, the volume of the pyramid is:
V = (1/3)(9 in.2)(3 in.)
V = 9 in.3
Therefore, the volume of the pyramid is 9 in.3.
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