A conical circus tent is to be made of canvas. The height of the tent is 35 m and the radius of the base is 84 m. If `pi =(22)/7`, then the canvas required is :

Options

A. `24000 m^(2) `
B. `24004 m^(2) `
C. `24014 m^(2) `
D. `24024 m^(2)`

Answer

To find the canvas required for the conical circus tent, we need to calculate the curved surface area of the 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 of the base,
- \( L \) is the slant height of the cone.

### Step 1: Calculate the Slant Height (L)

The slant height \( L \) can be calculated using the Pythagorean theorem:

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

where:
- \( r = 84 \, \text{m} \) (radius),
- \( h = 35 \, \text{m} \) (height).

Calculating \( L \):

\[ L = \sqrt{(84)^2 + (35)^2} \]

Calculating \( 84^2 \):

\[ 84^2 = 7056 \]

Calculating \( 35^2 \):

\[ 35^2 = 1225 \]

Now, adding these values:

\[ L = \sqrt{7056 + 1225} = \sqrt{8281} \]

Calculating the square root:

\[ L = 91 \, \text{m} \]

### Step 2: Calculate the Curved Surface Area (CSA)

Now that we have \( L \), we can substitute the values into the CSA formula:

\[ \text{CSA} = \pi r L \]

Substituting \( \pi = \frac{22}{7} \), \( r = 84 \, \text{m} \), and \( L = 91 \, \text{m} \):

\[ \text{CSA} = \frac{22}{7} \times 84 \times 91 \]

Calculating \( \frac{22}{7} \times 84 \):

\[ \frac{22 \times 84}{7} = 22 \times 12 = 264 \]

Now, substituting this back into the CSA formula:

\[ \text{CSA} = 264 \times 91 \]

Calculating \( 264 \times 91 \):

\[ 264 \times 91 = 24024 \, \text{m}^2 \]

### Final Answer

The canvas required for the conical circus tent is:

\[ \text{Canvas required} = 24024 \, \text{m}^2 \]