To calculate the volume of the rectangular pyramid, we can use the formula for the volume of a pyramid:
Volume = (1/3) × base area × height
Since the pyramid has a rectangular base, the base area can be calculated as length × width. Let's assume the length of the base is l, the width is w, and the height of the pyramid is h:
Volume = (1/3) × lw × h
Given that the volume of the pyramid is 480 in^3, we can set up the equation:
480 = (1/3)lw × h
Now, we know that the base and height of the rectangular prism are congruent to the pyramid, meaning the base area (l × w) and height (h) of the prism are the same as the pyramid. Therefore, the volume of the prism can be calculated using the same formula for the volume of a rectangular prism:
Volume = l × w × h
Given that the volume of the prism is 1440 in^3, we can set up the equation:
1440 = lw × h
We can now solve these two equations simultaneously by substituting the value of lw × h from the first equation into the second equation:
lw × h = 480
1440 = 480
Therefore, the volume of the rectangular prism is equal to 1440 in^3.
Explain how 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 equals 1,440.
9 answers
shorter bruv
Sure! Since the volume of the rectangular pyramid is 480 in^3, the volume of the rectangular prism with the same base and height dimensions will be 1440 in^3.
explain
Apologies for the confusion!
To find the volume of a rectangular pyramid, we use the formula:
Volume = 1/3 × base area × height
Given that the volume of the rectangular pyramid is 480 in^3, and assuming the base of the pyramid has dimensions of length (l) and width (w), and the height of the pyramid is h, we can express this formula as:
480 = 1/3 × lw × h
Since the rectangular prism has the same base and height dimensions as the pyramid, its volume can be calculated as:
Volume = l × w × h
Given that the volume of the rectangular prism is 1440 in^3, we can set this volume equal to lw × h (from the pyramid volume equation):
1440 = lw × h
Therefore, we can conclude that the volume of the rectangular prism, with the same base and height dimensions as the pyramid, is 1440 in^3.
To find the volume of a rectangular pyramid, we use the formula:
Volume = 1/3 × base area × height
Given that the volume of the rectangular pyramid is 480 in^3, and assuming the base of the pyramid has dimensions of length (l) and width (w), and the height of the pyramid is h, we can express this formula as:
480 = 1/3 × lw × h
Since the rectangular prism has the same base and height dimensions as the pyramid, its volume can be calculated as:
Volume = l × w × h
Given that the volume of the rectangular prism is 1440 in^3, we can set this volume equal to lw × h (from the pyramid volume equation):
1440 = lw × h
Therefore, we can conclude that the volume of the rectangular prism, with the same base and height dimensions as the pyramid, is 1440 in^3.
smaller
The volume of a rectangular pyramid is 480 in^3. The volume of a rectangular prism with the same base and height dimensions is 1440 in^3.
how
If a rectangular pyramid has a volume of 480 in^3, it means that the amount of space the pyramid occupies is 480 cubic inches. A rectangular prism with the same base and height dimensions as the pyramid will have a greater volume because a prism is a solid figure that takes up more space than a pyramid.
Since a rectangular prism has a volume that is three times that of a pyramid with the same base and height dimensions, the volume of the prism is calculated as follows:
Volume of Prism = 3 × Volume of Pyramid
Volume of Prism = 3 × 480 in^3
Volume of Prism = 1440 in^3
Therefore, the volume of the rectangular prism is 1440 in^3.
Since a rectangular prism has a volume that is three times that of a pyramid with the same base and height dimensions, the volume of the prism is calculated as follows:
Volume of Prism = 3 × Volume of Pyramid
Volume of Prism = 3 × 480 in^3
Volume of Prism = 1440 in^3
Therefore, the volume of the rectangular prism is 1440 in^3.
1 answer