calculate missing dimension.
square based pyramid has height 92cm and volume 5.4 m cube.
Vol. = 1/3 (base area)(height)
Base area = side^2
Converting to same units:
5.4 = 1/3(side^2)(.92)
Solve for "side."
To calculate the missing dimension, we need to use the formula for the volume of a square-based pyramid:
Volume = (1/3) * Base Area * Height
First, let's convert the volume from cubic meters to cubic centimeters:
5.4 m^3 = 5.4 * 1000000 cm^3 = 5400000 cm^3
Now, the volume is known as 5400000 cm^3, and the height is given as 92 cm. We need to find the base area.
Using the volume formula, rearranged to solve for the base area:
Base Area = (3 * Volume) / (Height)
Base Area = (3 * 5400000) / 92
Base Area = 16200000 / 92
Base Area ≈ 176086.96 cm^2
Since a square-based pyramid has a square base, we can find the length of one side of the square base by taking the square root of the base area:
Length of one side of the square base = √Base Area
Length of one side of the square base = √176086.96 cm^2
Length of one side of the square base ≈ 419.66 cm
Therefore, the missing dimension (length of one side of the square base) is approximately 419.66 cm.
To calculate the missing dimension of the square-based pyramid, we need to use the formula for the volume of a pyramid.
The formula for the volume of a pyramid is:
V = (1/3) * base_area * height
In this case, we already have the height of the pyramid, which is 92 cm. We also know the volume of the pyramid, which is given as 5.4 m^3. However, the side or base area of the square base is missing, which we need to find.
To find the base area, we need to rearrange the formula for volume:
base_area = (3 * V) / height
First, we need to convert the volume from cubic meters to cubic centimeters since the height is given in centimeters.
Given:
Height (h) = 92 cm
Volume (V) = 5.4 m^3
Converting the volume:
5.4 m^3 = 5400 cm^3 (1 m^3 = 1,000,000 cm^3)
Now, substituting the values into the rearranged formula for base area:
base_area = (3 * 5400) / 92
base_area ≈ 163.04 cm^2
Therefore, the missing dimension, which is the side length or base area of the square base, is approximately 163.04 cm^2.