The curved surface area and the diameter of a right circular cylinder and `660 cm^(2)` and 21 cm. respectively. Find its height (in cm.).

Options

A. 9
B. 10
C. 12
D. 8

Answer

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

### Step 1: Identify the given values
- Curved Surface Area (CSA) = 660 cm²
- Diameter (d) = 21 cm

### Step 2: Calculate the radius (r)
The radius is half of the diameter.
\[ r = \frac{d}{2} = \frac{21 \text{ cm}}{2} = 10.5 \text{ cm} \]

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

### Step 4: Substitute the known values into the formula
Substituting the values we have:
\[ 660 = 2 \times \frac{22}{7} \times 10.5 \times h \]

### Step 5: Simplify the equation
First, calculate \( 2 \times \frac{22}{7} \times 10.5 \):
\[ 2 \times \frac{22}{7} \times 10.5 = \frac{44 \times 10.5}{7} = \frac{462}{7} = 66 \]
Now, substitute this back into the equation:
\[ 660 = 66h \]

### Step 6: Solve for height (h)
To find \( h \), divide both sides by 66:
\[ h = \frac{660}{66} = 10 \text{ cm} \]

### Final Answer
The height of the cylinder is \( 10 \text{ cm} \).

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