The curved surface area of the cone of radius 5 cm and height 12 cm is

Options

A. `60 pi cm^(2)`
B. `65 pi cm ^(2)`
C. `300pi cm^(2)`
D. `325 pi cm^(2)`

Answer

To find the curved surface area of a cone with a radius of 5 cm and a height of 12 cm, we can follow these steps:

### Step 1: Identify the formula for the curved surface area of a cone.
The formula for the curved surface area (CSA) of a cone is given by:
\[ \text{CSA} = \pi r l \]
where \( r \) is the radius and \( l \) is the slant height of the cone.

### Step 2: Calculate the slant height \( l \).
The slant height can be calculated using the Pythagorean theorem:
\[ l = \sqrt{r^2 + h^2} \]
where \( h \) is the height of the cone.

Given:
- \( r = 5 \, \text{cm} \)
- \( h = 12 \, \text{cm} \)

Substituting the values:
\[ l = \sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13 \, \text{cm} \]

### Step 3: Substitute the values into the CSA formula.
Now that we have the slant height, we can substitute \( r \) and \( l \) into the CSA formula:
\[ \text{CSA} = \pi \times 5 \times 13 \]

### Step 4: Use the value of \( \pi \).
Using \( \pi \approx \frac{22}{7} \):
\[ \text{CSA} = \frac{22}{7} \times 5 \times 13 \]

### Step 5: Calculate the CSA.
First, calculate \( 5 \times 13 = 65 \):
\[ \text{CSA} = \frac{22}{7} \times 65 \]

Now, multiply \( 22 \) by \( 65 \):
\[ 22 \times 65 = 1430 \]

Finally, divide by \( 7 \):
\[ \text{CSA} = \frac{1430}{7} \approx 204.2857 \, \text{cm}^2 \]

### Step 6: Round the answer.
Rounding to two decimal places, the curved surface area of the cone is approximately:
\[ \text{CSA} \approx 204.29 \, \text{cm}^2 \]

### Final Answer:
The curved surface area of the cone is approximately **204.29 cm²**.

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