The volume of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height.
Given that the volume of the rectangular prism is 27 in.³, we can rewrite this as:
27 = lwh
Since the base and height of the rectangular pyramid are congruent to the prism, the base area of the pyramid is the same as the base area of the prism, which is lw.
The volume of a rectangular pyramid is given by the formula V = (1/3)Bh, where B is the base area and h is the height of the pyramid.
Substituting the base area B = lw into the formula, we get:
V = (1/3)(lw)h
Since the base and height are congruent to the prism, we know that h = l, w = l. Therefore, we can rewrite the formula as:
V = (1/3)(l²)(l) = (1/3)l³
Substitute 27 for the volume of the prism into the formula, we get:
27 = (1/3)l³
Multiplying both sides by 3, we get:
81 = l³
Taking the cube root of both sides, we find:
l = 3
Therefore, the volume of the rectangular pyramid is:
V = (1/3)(3²)(3) = 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? (1 point)
3 answers
A rectangular pyramid has a volume of 480 in.³. If a rectangular prism has a base and height congruent to the pyramid, what is the volume of the prism? (1 point)
The volume of a rectangular pyramid is given by the formula V = (1/3)Bh, where B is the base area and h is the height of the pyramid.
Given that the volume of the rectangular pyramid is 480 in.³, we have:
480 = (1/3)Bh
Since the base and height of the rectangular prism are congruent to the pyramid, the base area of the prism is the same as the base area of the pyramid, which is B.
The volume of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height of the prism.
Substituting B for lw into the formula, we get:
V = Bh = lwh
Since the base and height are congruent to the pyramid, we know that h = l, w = l. Therefore, we can rewrite the formula as:
V = l²h
Substitute 480 for the volume of the pyramid into the formula, we get:
480 = l²h
But we also know that h = l from the given information about the congruence of the base and height, so we can substitute h = l into the equation:
480 = l³
Taking the cube root of both sides, we find:
l = 8
Therefore, the volume of the rectangular prism is:
V = (8)(8)(8) = 512 in.³.
So, the volume of the prism is 512 in.³.
Given that the volume of the rectangular pyramid is 480 in.³, we have:
480 = (1/3)Bh
Since the base and height of the rectangular prism are congruent to the pyramid, the base area of the prism is the same as the base area of the pyramid, which is B.
The volume of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height of the prism.
Substituting B for lw into the formula, we get:
V = Bh = lwh
Since the base and height are congruent to the pyramid, we know that h = l, w = l. Therefore, we can rewrite the formula as:
V = l²h
Substitute 480 for the volume of the pyramid into the formula, we get:
480 = l²h
But we also know that h = l from the given information about the congruence of the base and height, so we can substitute h = l into the equation:
480 = l³
Taking the cube root of both sides, we find:
l = 8
Therefore, the volume of the rectangular prism is:
V = (8)(8)(8) = 512 in.³.
So, the volume of the prism is 512 in.³.