A rectangular Pyramid has a volume of 22,750cm. One of the dimensions of the base is 30 cm, and the altitude is 65 cm. What is the other dimension of the Pyramid's base? Round the answer to the nearest hundredth if necessary.
We can use the formula for the volume of a pyramid:
V = (1/3)Bh
where B is the area of the base, h is the height (altitude), and V is the volume.
We know that V = 22,750 cm^3 and h = 65 cm. We also know that one dimension of the base is 30 cm (we'll call this length a), so the area of the base (B) is:
B = a x b
where b is the other dimension of the base.
We can rewrite the formula for the volume of the pyramid as:
B = (3V)/h
Plugging in the values we know:
b = (3(22,750 cm^3))/65 cm
b ≈ 263.08 cm
Rounding to the nearest hundredth:
b ≈ 263.08 cm ≈ 263.09 cm
Therefore, the other dimension of the pyramid's base is approximately 263.09 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 that the volume of the pyramid is 22,750 cm³, the height is 65 cm, and one of the dimensions of the base is 30 cm, we can plug these values into the formula:
22,750 = (1/3) * Base Area * 65
To solve for the base area, we can rearrange the formula:
Base Area = (22,750 * 3) / 65
Base Area ≈ 1058.46 cm²
Now, let's find the other dimension of the base. Since the base area of a rectangle is equal to the length multiplied by the width, and we already know that one of the dimensions is 30 cm, we can divide the base area by 30 cm to find the other dimension:
Other Dimension = Base Area / One Dimension
Other Dimension ≈ 1058.46 cm² / 30 cm
Other Dimension ≈ 35.28 cm
Therefore, the other dimension of the pyramid's base is approximately 35.28 cm.