To find the diameter and height of the cylindrical pillar, we can use the formulas for the curved surface area and volume of a cylinder.
The curved surface area (CSA) of a cylinder is given by the formula:
CSA = 2πrh
And the volume (V) of a cylinder is given by:
V = πr²h
Here, we know that:
- CSA = 264 m²
- V = 9243 m³
From the CSA formula, we can express h in terms of r:
h = CSA / (2πr)
Substituting CSA = 264 m², we get:
h = 264 / (2πr) = 132 / (πr)
Now we can substitute this expression for h into the volume formula:
V = πr²(132 / (πr))
This simplifies to:
V = 132r
Now, we know V = 9243 m³, so we can set up the equation:
132r = 9243
Solving for r, we find:
r = 9243 / 132
r ≈ 69.96 m
Now that we have the radius, we can find the height using our earlier equation for h:
h = 132 / (π × 69.96)
h ≈ 0.60 m
To find the diameter, we simply double the radius:
Diameter = 2r ≈ 139.92 m
Thus, the diameter of the pillar is approximately 139.92 m, and the height is approximately 0.60 m.