In the making of a right circular cone whose base radius is 7 cm and altitude is 24 cm. How many area of iron sheet is required ? (Take `pi = (22)/(7))`

Options

A. `708 cm ^(2)`
B. `804 cm ^(2)`
C. `704 cm ^(2)`
D. `408 cm ^(2)`

Answer

To find the area of iron sheet required to make a right circular cone with a base radius of 7 cm and an altitude of 24 cm, we need to calculate the total surface area of the cone, which includes the curved surface area and the area of the base.

### Step 1: Calculate the Slant Height (L)
To find the slant height (L) of the cone, we can use the Pythagorean theorem. The formula is:
\[ L = \sqrt{r^2 + h^2} \]
where \( r \) is the radius and \( h \) is the height (altitude).

Given:
- Radius \( r = 7 \) cm
- Height \( h = 24 \) cm

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

### Step 2: Calculate the Curved Surface Area (CSA)
The formula for the curved surface area of a cone is:
\[ \text{CSA} = \pi r L \]

Using \( \pi = \frac{22}{7} \):
\[ \text{CSA} = \frac{22}{7} \times 7 \times 25 \]

Now, simplifying:
\[ \text{CSA} = 22 \times 25 \]
\[ \text{CSA} = 550 \text{ cm}^2 \]

### Step 3: Calculate the Area of the Base
The area of the base of the cone is given by:
\[ \text{Area of Base} = \pi r^2 \]

Calculating:
\[ \text{Area of Base} = \frac{22}{7} \times 7^2 \]
\[ \text{Area of Base} = \frac{22}{7} \times 49 \]

Now, simplifying:
\[ \text{Area of Base} = 22 \times 7 \]
\[ \text{Area of Base} = 154 \text{ cm}^2 \]

### Step 4: Calculate the Total Surface Area
The total surface area of the cone is the sum of the curved surface area and the area of the base:
\[ \text{Total Surface Area} = \text{CSA} + \text{Area of Base} \]
\[ \text{Total Surface Area} = 550 + 154 \]
\[ \text{Total Surface Area} = 704 \text{ cm}^2 \]

### Final Answer
The area of iron sheet required is:
\[ \text{Total Area} = 704 \text{ cm}^2 \]

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