What is the volume of a rectangular pyramid that has a center of 5 mm a base of 7 mm and a side of 7.5 mm
To find the volume of a rectangular pyramid, you can use the formula:
V = (1/3) * base area * height
First, let's find the base area of the pyramid. Since the base is a rectangle, the area is given by length * width:
Base area = 7 mm * 7.5 mm = 52.5 mm²
Next, we need to find the height of the pyramid. The height can be found using the Pythagorean theorem, as it forms a right triangle with the center point, half the base, and the side of the pyramid.
The height can be calculated as follows:
h² = c² - a²
h² = 7.5² - (7/2)²
h² = 56.25 - 12.25
h² = 44
h = √44
h ≈ 6.63 mm
Now, substitute the base area and height into the volume formula:
V = (1/3) * 52.5 mm² * 6.63 mm
V ≈ 115.97 mm³
Therefore, the volume of the rectangular pyramid is approximately 115.97 mm³.