The height and the slant height of a right circular cone are 24 cm and 25 cm ,respectively . Considering `pi` as `(22)/(7)` ,find the curved surface area of the cone .

Options

A. `550 cm^(2)`
B. `572 cm^(2)`
C. `528 cm^(2)`
D. `539 cm^(2)`

Answer

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

### Step 1: Identify the given values
- Height (h) = 24 cm
- Slant height (l) = 25 cm
- π (pi) = 22/7

### Step 2: Use the Pythagorean theorem to find the radius (r)
The relationship between the height, radius, and slant height of a cone is given by the formula:
\[ l^2 = h^2 + r^2 \]

Substituting the known values:
\[ 25^2 = 24^2 + r^2 \]
\[ 625 = 576 + r^2 \]

### Step 3: Solve for r²
Rearranging the equation:
\[ r^2 = 625 - 576 \]
\[ r^2 = 49 \]

### Step 4: Calculate r
Taking the square root of both sides:
\[ r = \sqrt{49} \]
\[ r = 7 \text{ cm} \]

### Step 5: 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 of π, r, and l:
\[ \text{CSA} = \frac{22}{7} \times 7 \times 25 \]

### Step 6: Simplify the expression
The 7 in the numerator and denominator cancels out:
\[ \text{CSA} = 22 \times 25 \]

### Step 7: Calculate the final value
\[ \text{CSA} = 550 \text{ cm}^2 \]

### Final Answer
The curved surface area of the cone is **550 cm²**.

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