The height of a cylinder is 15 cm, its curved surface area is 660 sq cm. Find its diameter.

Answer

To find the diameter of the cylinder given its height and curved surface area, we will follow these steps:

### Step 1: Write down the formula for the curved surface area (CSA) of a cylinder.
The formula for the curved surface area (CSA) of a cylinder is given by:
\[ \text{CSA} = 2\pi rh \]
where \( r \) is the radius and \( h \) is the height of the cylinder.

### Step 2: Substitute the known values into the formula.
We know that the height \( h = 15 \) cm and the curved surface area \( \text{CSA} = 660 \) cm². Substituting these values into the formula gives:
\[ 660 = 2 \times \frac{22}{7} \times r \times 15 \]

### Step 3: Simplify the equation.
First, simplify the right side:
\[ 660 = \frac{44}{7} \times r \times 15 \]
Calculating \( \frac{44}{7} \times 15 \):
\[ \frac{44 \times 15}{7} = \frac{660}{7} \]
So, the equation becomes:
\[ 660 = \frac{660}{7} \times r \]

### Step 4: Solve for \( r \).
To isolate \( r \), multiply both sides by \( 7 \):
\[ 660 \times 7 = 660 \times r \]
This simplifies to:
\[ 4620 = 660r \]
Now, divide both sides by \( 660 \):
\[ r = \frac{4620}{660} \]
Calculating this gives:
\[ r = 7 \text{ cm} \]

### Step 5: Find the diameter.
The diameter \( d \) of the cylinder is given by:
\[ d = 2r \]
Substituting the value of \( r \):
\[ d = 2 \times 7 = 14 \text{ cm} \]

### Final Answer:
The diameter of the cylinder is \( 14 \) cm.

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