The slant height of a right circular cone is 15 m and its height is 9 m. The area of its curved surface, is:

Options

A. `169 pi m^2`
B. `172 pi m^2`
C. `165 pi m^2`
D. `180 pi m^2`

Answer

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

### Step 1: Identify the given values
We are given:
- Slant height (l) = 15 m
- Height (h) = 9 m

### Step 2: Use the Pythagorean theorem to find the radius (r)
In a right circular cone, the relationship between the radius (r), height (h), and slant height (l) can be expressed using the Pythagorean theorem:
\[ l^2 = r^2 + h^2 \]

Substituting the known values:
\[ 15^2 = r^2 + 9^2 \]
\[ 225 = r^2 + 81 \]

### Step 3: Solve for r
Now, we can isolate r^2:
\[ r^2 = 225 - 81 \]
\[ r^2 = 144 \]

Taking the square root of both sides gives us:
\[ r = \sqrt{144} = 12 \text{ m} \]

### Step 4: Calculate the curved surface area (CSA)
The formula for the curved surface area of a cone is:
\[ \text{CSA} = \pi r l \]

Substituting the values we have:
\[ \text{CSA} = \pi \times 12 \times 15 \]
\[ \text{CSA} = 180\pi \text{ m}^2 \]

### Step 5: Provide the final answer
The area of the curved surface of the cone is:
\[ \text{CSA} \approx 180 \times 3.14 \approx 565.2 \text{ m}^2 \]
(Using \(\pi \approx 3.14\))

### Final Answer:
The area of the curved surface is approximately \( 565.2 \text{ m}^2 \).

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