You can find the radius of a cylinder if you know its curved surface area and its height by using the formula for the curved surface area and rearranging it to solve for the radius.
Understanding the Formula
The curved surface area (CSA) of a cylinder is the area of its side wall, excluding the top and bottom circles. The formula for the curved surface area of a cylinder is:
CSA = 2πrh
Where:
- π (Pi) is a mathematical constant, approximately equal to 22/7 or 3.14159.
- r is the radius of the base (and top) of the cylinder.
- h is the height of the cylinder.
Steps to Calculate the Radius
To find the radius (r) when you are given the curved surface area (CSA) and the height (h), you need to rearrange the formula:
- Start with the formula: CSA = 2πrh
- Isolate 'r' by dividing both sides of the equation by 2πh: r = CSA / (2πh)
Example Calculation Using Provided Data
Let's apply this method using the information from the provided reference:
Given Information
- Height (h) = 16 cm
- Curved Surface Area (CSA) = 352 cm²
Applying the Formula
The formula for the curved surface area of a cylinder is 2πrh.
We are given that the Curved Surface area = 352 cm².
So, we set the formula equal to the given area:
2πrh = 352
Solving for Radius
Now, substitute the known values into the equation and solve for 'r'. Using the approximation π = 22/7 as shown in the reference:
-
Substitute h = 16 cm and π = 22/7 into the equation:
2 × (22/7) × r × 16 = 352 -
Rearrange the equation to solve for r:
r = 352 / (2 × (22/7) × 16) -
Perform the calculation:
r = 352 × (7 / (2 × 22 × 16))
r = 352 × (7 / (44 × 16))
r = 352 × (7 / 704)
r = (352 / 704) × 7
r = (1/2) × 7
r = 7/2
r = 3.5 cm
Hence, based on the given curved surface area and height, the radius of the cylinder is found to be 3.5 cm.
Key Takeaway
To find the radius of a cylinder when its curved surface area and height are known, simply divide the curved surface area by twice the product of pi and the height (r = CSA / (2πh)).
