If the curved surface area of a cylinder is `1760 cm^(2)` and its base radius is 14 cm then its height is

Options

A. 10 cm
B. 15 cm
C. 20 cm
D. 40 cm

Explanation

To find the height of the cylinder given its curved surface area and base radius, we can follow these steps:

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

### Step 2: Substitute the known values into the formula.
We know:
- Curved Surface Area (CSA) = \( 1760 \, \text{cm}^2 \)
- Radius \( r = 14 \, \text{cm} \)

Substituting these values into the formula:
\[ 1760 = 2 \pi (14) h \]

### Step 3: Simplify the equation.
Now, we can simplify the equation. First, calculate \( 2 \pi (14) \):
\[ 2 \pi (14) = 28 \pi \]
So the equation becomes:
\[ 1760 = 28 \pi h \]

### Step 4: Solve for \( h \).
To isolate \( h \), we divide both sides by \( 28 \pi \):
\[ h = \frac{1760}{28 \pi} \]

### Step 5: Substitute the value of \( \pi \).
Using \( \pi \approx \frac{22}{7} \):
\[ h = \frac{1760}{28 \times \frac{22}{7}} = \frac{1760 \times 7}{28 \times 22} \]

### Step 6: Simplify further.
Now, simplify \( \frac{1760 \times 7}{28 \times 22} \):
\[ h = \frac{12320}{616} \]

### Step 7: Divide to find \( h \).
Calculating \( \frac{12320}{616} \):
\[ h = 20 \, \text{cm} \]

### Final Answer:
Thus, the height of the cylinder is \( 20 \, \text{cm} \).

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