A rectangular Pyramid base has a volume of 22,750 cm. One of the base is 30 cm, and the altitude is 65 cm. What is the other dimension of the Pyramid's base?
We can use the formula for the volume of a rectangular pyramid:
V = (1/3)Bh
where B is the area of the base and h is the altitude.
We are given V = 22,750 cm³, h = 65 cm, and one base dimension is 30 cm. Let's call the other base dimension x.
To find the area of the base, we can use the formula for the area of a rectangle:
B = lw
where l and w are the length and width of the base.
We are given w = 30 cm and we need to find l.
To do this, we can use the fact that the area of the base is equal to lw:
B = lw
B = 30l
Substituting this into the formula for the volume of a rectangular pyramid, we get:
V = (1/3)Bh
22,750 = (1/3)(30l)(65)
22,750 = 650l
l = 35 cm
Therefore, the other base dimension of the pyramid is 35 cm.
To find the other dimension of the pyramid's base, we can use the formula for the volume of a rectangular pyramid:
Volume = (1/3) * base area * height
Given:
Volume = 22,750 cm³
Altitude/height = 65 cm
We need to find the base area, which is the area of one of the base's dimensions.
Let's substitute the known values into the formula:
22,750 cm³ = (1/3) * base area * 65 cm
To isolate the base area, we can rearrange the equation:
base area = (22,750 cm³ / (1/3)) / 65 cm
base area = (22,750 cm³ * 3) / 65 cm
base area = 114,750 cm²
Since the pyramid's base is rectangular, we know that the area of a rectangle is the product of its dimensions (length * width). One of the dimensions is given as 30 cm. Let the other dimension be "x" cm.
So, we can write the following equation:
length * width = 114,750 cm²
30 cm * x cm = 114,750 cm²
Solving for x:
x = 114,750 cm² / 30 cm
x = 3825 cm
Therefore, the other dimension of the pyramid's base is 3825 cm.