The volume of a rectangular prism is given by the formula V = l * w * h, where l is the length, w is the width, and h is the height.
Given that the volume of the prism is 27 in.3, let's assume that the base of the prism has dimensions of x by x and the height of the prism is also x (since the base and height of the pyramid are congruent to the prism).
Therefore, the volume of the prism is x * x * x = 27
x^3 = 27
x = 3
So, the dimensions of the base of the pyramid are 3 by 3 and the height of the pyramid is also 3. The volume of a rectangular pyramid is given by the formula V = (1/3) * l * w * h.
Substitute the dimensions of the pyramid:
V = (1/3) * 3 * 3 * 3
V = 27/3
V = 9
Therefore, the volume of the rectangular pyramid is 9 in.3.
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?
? in.3
3 answers
are you sure
My apologies for the mistake in the previous calculation. Let me correct it.
Given that the volume of the rectangular prism is 27 in.3, and the dimensions of the base and height of the rectangular prism are equal, we can denote each side of the base of the prism as x and the height of the prism as x.
The volume of the prism is given by V = l * w * h, where l is the length, w is the width, and h is the height.
Therefore, V = x * x * x
V = x^3 = 27
x = 3
So, the length, width, and height of the prism are all 3 units.
Now, the volume of a rectangular pyramid is given by V = (1/3) * l * w * h.
For the pyramid with base and height dimensions congruent to the prism:
V = (1/3) * 3 * 3 * 3
V = (1/3) * 27
V = 9 in.3
Therefore, the volume of the rectangular pyramid with base and height dimensions congruent to the prism is 9 in.3. Thank you for bringing that to my attention.
Given that the volume of the rectangular prism is 27 in.3, and the dimensions of the base and height of the rectangular prism are equal, we can denote each side of the base of the prism as x and the height of the prism as x.
The volume of the prism is given by V = l * w * h, where l is the length, w is the width, and h is the height.
Therefore, V = x * x * x
V = x^3 = 27
x = 3
So, the length, width, and height of the prism are all 3 units.
Now, the volume of a rectangular pyramid is given by V = (1/3) * l * w * h.
For the pyramid with base and height dimensions congruent to the prism:
V = (1/3) * 3 * 3 * 3
V = (1/3) * 27
V = 9 in.3
Therefore, the volume of the rectangular pyramid with base and height dimensions congruent to the prism is 9 in.3. Thank you for bringing that to my attention.
1 answer