If the curved surface area of a cylinder is 1320 `cm^2` and its base has diameter 21 cm, then the height of the cylinder is

Options

A. 10 cm
B. 20 cm
C. 22 cm
D. 25 cm

Answer

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

### Step 1: Identify the given values
- Curved Surface Area (CSA) of the cylinder = 1320 cm²
- Diameter of the base = 21 cm

### Step 2: Calculate the radius
The radius (R) can be calculated from the diameter using the formula:
\[ R = \frac{\text{Diameter}}{2} \]
Substituting the given diameter:
\[ R = \frac{21 \text{ cm}}{2} = 10.5 \text{ cm} \]

### Step 3: Use the formula for the curved surface area of a cylinder
The formula for the curved surface area (CSA) of a cylinder is:
\[ \text{CSA} = 2 \pi R H \]
Where:
- \( \pi \) is approximately \( \frac{22}{7} \)
- \( H \) is the height of the cylinder

### Step 4: Substitute the known values into the formula
We can substitute the values we have into the CSA formula:
\[ 1320 = 2 \times \frac{22}{7} \times 10.5 \times H \]

### Step 5: Simplify the equation
First, calculate \( 2 \times \frac{22}{7} \times 10.5 \):
\[ 2 \times \frac{22}{7} \times 10.5 = \frac{44 \times 10.5}{7} = \frac{462}{7} \]
So we can rewrite the equation as:
\[ 1320 = \frac{462}{7} \times H \]

### Step 6: Solve for H
To isolate \( H \), multiply both sides by \( \frac{7}{462} \):
\[ H = 1320 \times \frac{7}{462} \]
Now, simplify \( \frac{1320}{462} \):
\[ \frac{1320}{462} = \frac{220}{77} = \frac{20}{7} \]
Thus:
\[ H = 20 \times 7 = 140 \text{ cm} \]

### Step 7: Final calculation
Now we can calculate \( H \):
\[ H = 20 \text{ cm} \]

### Conclusion
The height of the cylinder is \( 20 \text{ cm} \).

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