The curved surface area and the height of a right circular cylinder are `660 cm^(2)` and 10 cm respectively. Find its diameter (in cm).

Options

A. 14
B. `10.5`
C. 21
D. `17.5`

Answer

To find the diameter of a right circular cylinder given the curved surface area (CSA) and height, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the formula for the curved surface area of a cylinder**:
The formula for the curved surface area (CSA) of a right circular cylinder is given by:
\[ \text{CSA} = 2 \pi r h \]
where \( r \) is the radius and \( h \) is the height of the cylinder.

2. **Substitute the known values**:
We know that the CSA is \( 660 \, \text{cm}^2 \) and the height \( h \) is \( 10 \, \text{cm} \). Substitute these values into the formula:
\[ 660 = 2 \pi r \times 10 \]

3. **Simplify the equation**:
We can simplify the equation:
\[ 660 = 20 \pi r \]

4. **Solve for \( r \)**:
To isolate \( r \), divide both sides by \( 20 \pi \):
\[ r = \frac{660}{20 \pi} \]
Now, substituting \( \pi \) with \( \frac{22}{7} \):
\[ r = \frac{660}{20 \times \frac{22}{7}} = \frac{660 \times 7}{20 \times 22} \]

5. **Calculate the value of \( r \)**:
First, simplify \( \frac{660 \times 7}{20 \times 22} \):
\[ r = \frac{4620}{440} \]
Now, simplify \( \frac{4620}{440} \):
\[ r = \frac{462}{44} = \frac{231}{22} = 10.5 \, \text{cm} \]

6. **Find the diameter**:
The diameter \( D \) is twice the radius:
\[ D = 2r = 2 \times 10.5 = 21 \, \text{cm} \]

### Final Answer:
The diameter of the cylinder is \( 21 \, \text{cm} \).