The curved surface area and the diameter of a right circular cylinder are `352 cm^2` and 14 cm respectively. Find its height (in cm).

Options

A. 9
B. 8
C. 10
D. 11

Answer

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

### Step 1: Understand the given information
We know:
- Curved Surface Area (CSA) of the cylinder = 352 cm²
- Diameter of the cylinder = 14 cm

### Step 2: Find the radius of the cylinder
The radius (r) can be calculated from the diameter using the formula:
\[ r = \frac{\text{Diameter}}{2} \]
Substituting the given diameter:
\[ r = \frac{14 \text{ cm}}{2} = 7 \text{ cm} \]

### Step 3: Write the formula for the curved surface area of a cylinder
The formula for the curved surface area (CSA) of a right circular cylinder is:
\[ \text{CSA} = 2 \pi r h \]
Where:
- \( r \) is the radius
- \( h \) is the height
- \( \pi \) is approximately \( \frac{22}{7} \)

### Step 4: Substitute the known values into the formula
Substituting the values we have:
\[ 352 = 2 \times \frac{22}{7} \times 7 \times h \]

### Step 5: Simplify the equation
First, simplify the left side:
\[ 352 = 2 \times \frac{22}{7} \times 7 \times h \]
The \( 7 \) in the numerator and denominator cancels out:
\[ 352 = 2 \times 22 \times h \]
Now calculate \( 2 \times 22 \):
\[ 352 = 44h \]

### Step 6: Solve for height (h)
To find \( h \), divide both sides of the equation by 44:
\[ h = \frac{352}{44} \]
Calculating the right side:
\[ h = 8 \text{ cm} \]

### Final Answer
The height of the cylinder is **8 cm**.

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