The perimeter of base of a right circular cone is 44 cm. If the height of the cone is 24 cm, then what is the curved surface area ( in `cm^(2)`) of the cone ?

Options

A. 550
B. 1100
C. 2200
D. 650

Answer

To find the curved surface area of a right circular cone, we can follow these steps:

### Step 1: Find the radius of the base of the cone
The perimeter (circumference) of the base of the cone is given as 44 cm. The formula for the circumference of a circle is:

\[ C = 2\pi r \]

Substituting the value of the circumference:

\[ 44 = 2\pi r \]

To find the radius \( r \), we can rearrange the equation:

\[ r = \frac{44}{2\pi} \]

Using \( \pi \approx \frac{22}{7} \):

\[ r = \frac{44}{2 \times \frac{22}{7}} = \frac{44 \times 7}{44} = 7 \text{ cm} \]

### Step 2: Find the slant height of the cone
The height \( h \) of the cone is given as 24 cm. We can find the slant height \( l \) using the Pythagorean theorem:

\[ l = \sqrt{h^2 + r^2} \]

Substituting the values:

\[ l = \sqrt{24^2 + 7^2} = \sqrt{576 + 49} = \sqrt{625} = 25 \text{ cm} \]

### Step 3: Calculate the curved surface area
The formula for the curved surface area \( A \) of a cone is:

\[ A = \pi r l \]

Substituting the values of \( \pi \), \( r \), and \( l \):

\[ A = \frac{22}{7} \times 7 \times 25 \]

The \( 7 \) in the numerator and denominator cancels out:

\[ A = 22 \times 25 = 550 \text{ cm}^2 \]

### Final Answer
The curved surface area of the cone is \( 550 \text{ cm}^2 \).

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