If curved surface area of a cylinder is 1386 sq cm and height is 21 cm, what will be its radius ?
(Take `pi = (22)/(7)`)

Options

A. 21 cm
B. 5.25 cm
C. 10.5 cm
D. 15.75 cm

Answer

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

### Step 1: Write down 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 \( r \) is the radius and \( h \) is the height.

### Step 2: Substitute the known values into the formula.
We know the curved surface area is 1386 sq cm and the height is 21 cm. Substituting these values into the formula gives:
\[ 1386 = 2 \times \frac{22}{7} \times r \times 21 \]

### Step 3: Simplify the equation.
First, calculate \( 2 \times \frac{22}{7} \times 21 \):
\[ 2 \times \frac{22}{7} \times 21 = \frac{44 \times 21}{7} = \frac{924}{7} = 132 \]
Now, substitute this back into the equation:
\[ 1386 = 132r \]

### Step 4: Solve for \( r \).
To find \( r \), divide both sides by 132:
\[ r = \frac{1386}{132} \]

### Step 5: Calculate the value of \( r \).
Now, perform the division:
\[ r = \frac{1386 \div 6}{132 \div 6} = \frac{231}{22} = 10.5 \text{ cm} \]

### Final Result:
The radius of the cylinder is \( 10.5 \) cm.

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