Solve the problem. What is the volume of a rectangular pyramid with a base of 200 square meters and a height of 75 meters? Show your work. can you please do it like a semi-good at math 7th grader did it.
To find the volume of a rectangular pyramid, we use the formula V = (1/3)Bh, where B is the area of the base and h is the height of the pyramid.
First, we need to find the area of the base. The base is rectangular with a length of 200 meters and a width of an unknown measurement. Since we know the base area is 200 square meters, we can set up the equation:
200 = length x width
Since we don't know the width, we can choose a reasonable number. Let's say the width is 10 meters. So, the length would be:
200 = 200 x 10
200 = 2000
Since 200 is not equal to 2000, our initial guess was incorrect. Let's try another guess. Let's say the width is 20 meters.
200 = 20 x width
200 = 20w
10 = w
So, the width is 10 meters. Now we can calculate the area of the base:
Area = length x width
Area = 200 x 10
Area = 2000 square meters
Now, we can plug the base area and the height into the volume formula:
V = (1/3) x 2000 x 75
V = (1/3) x 150000
V = 50000 cubic meters
Therefore, the volume of the rectangular pyramid is 50000 cubic meters.