The slant height of a conical tent made of canvas is `(14)/(3) m `. The radius of tent is 2.5 m. The width of the canvas is 1.25 m . If the rate of canvas per metres is Rs. 33, then the total cost of the canvas required for the tent ( in Rs.) is :

Options

A. a. 726
B. b. 950
C. c. 960
D. d. 968

Answer

To find the total cost of the canvas required for the conical tent, we will follow these steps:

### Step 1: Calculate the Surface Area of the Conical Tent
The formula for the surface area (A) of a cone is given by:
\[ A = \pi r l \]
where:
- \( r \) is the radius of the base of the cone,
- \( l \) is the slant height of the cone.

Given:
- Radius \( r = 2.5 \, \text{m} \)
- Slant height \( l = \frac{14}{3} \, \text{m} \)

Substituting the values into the formula:
\[ A = \pi \times 2.5 \times \frac{14}{3} \]

### Step 2: Calculate the Area
Using \( \pi \approx \frac{22}{7} \):
\[ A = \frac{22}{7} \times 2.5 \times \frac{14}{3} \]

Calculating \( 2.5 \) as a fraction:
\[ 2.5 = \frac{5}{2} \]
So,
\[ A = \frac{22}{7} \times \frac{5}{2} \times \frac{14}{3} \]

Calculating the area:
\[ A = \frac{22 \times 5 \times 14}{7 \times 2 \times 3} \]
\[ A = \frac{1540}{42} = \frac{770}{21} \, \text{m}^2 \]

### Step 3: Calculate the Length of Canvas Required
The area of the canvas is given by:
\[ \text{Area of Canvas} = \text{Length} \times \text{Width} \]
Let the length of the canvas be \( x \) meters. The width of the canvas is given as \( 1.25 \, \text{m} \):
\[ \frac{770}{21} = x \times 1.25 \]

Now, solving for \( x \):
\[ x = \frac{770}{21 \times 1.25} \]

Calculating \( 1.25 \) as a fraction:
\[ 1.25 = \frac{5}{4} \]
So,
\[ x = \frac{770}{21 \times \frac{5}{4}} = \frac{770 \times 4}{21 \times 5} = \frac{3080}{105} \]

### Step 4: Calculate the Total Cost of the Canvas
The cost per meter of canvas is given as Rs. 33. Therefore, the total cost \( C \) is:
\[ C = x \times 33 \]

Substituting the value of \( x \):
\[ C = \frac{3080}{105} \times 33 \]

Calculating the total cost:
\[ C = \frac{3080 \times 33}{105} = \frac{101640}{105} = 968 \, \text{Rs} \]

### Final Answer
The total cost of the canvas required for the tent is Rs. 968.

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