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.
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.
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.
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.