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.
Since the rectangular prism has a volume of 150 cubic inches, we can set up the equation as follows:
150 = lwh
Since the rectangular pyramid has a congruent length, width, and height, the volume of the rectangular pyramid can be calculated using the formula V = (1/3)lwh, where l is the length, w is the width, and h is the height.
Substitute the value of 150 for V in the formula and solve for the volume of the rectangular pyramid:
150 = (1/3)lwh
450 = lwh
Therefore, the volume of the rectangular pyramid is 450 cubic inches.
If a rectangular prism has a volume of 150 cubic inches, what is the volume of a rectangular pyramid that has a congruent length, width, and height?
3 answers
bot explain it better for kids
Sure!
Let's imagine the rectangular prism as a block of wood that is shaped like a box. It has a volume of 150 cubic inches, which means if we were to fill it up with small cubes, we would need 150 of those small cubes to fill it completely.
Now, let's think about the rectangular pyramid. It is like a tent but with a square base and walls that slant upwards to form a point at the top.
If we were to make the rectangular pyramid using the same amount of material and with the same length, width, and height as the rectangular prism, the volume of the pyramid would be 450 cubic inches.
This is because the pyramid has less space inside compared to the box, even though they have the same measurements on the outside. So, the rectangular pyramid has a smaller volume compared to the rectangular prism even though they have congruent length, width, and height.
Let's imagine the rectangular prism as a block of wood that is shaped like a box. It has a volume of 150 cubic inches, which means if we were to fill it up with small cubes, we would need 150 of those small cubes to fill it completely.
Now, let's think about the rectangular pyramid. It is like a tent but with a square base and walls that slant upwards to form a point at the top.
If we were to make the rectangular pyramid using the same amount of material and with the same length, width, and height as the rectangular prism, the volume of the pyramid would be 450 cubic inches.
This is because the pyramid has less space inside compared to the box, even though they have the same measurements on the outside. So, the rectangular pyramid has a smaller volume compared to the rectangular prism even though they have congruent length, width, and height.
3 answers