The inner and outer radii of a circular track are respectively 21 m and 28 m. The cost of gravevelling the track at Rs. 5 per sq m is

Options

A. Rs. 1078
B. Rs. 2156
C. Rs. 4312
D. Rs. 5390

Answer

To solve the problem of finding the cost of graveling a circular track with inner and outer radii of 21 m and 28 m respectively, we will follow these steps:

### Step 1: Calculate the area of the outer circle
The formula for the area of a circle is given by:
\[ \text{Area} = \pi R^2 \]
where \( R \) is the radius of the circle. For the outer circle, the radius is 28 m.

Using \( \pi \approx \frac{22}{7} \):
\[ \text{Area of outer circle} = \pi (28)^2 = \frac{22}{7} \times 28^2 \]
Calculating \( 28^2 \):
\[ 28^2 = 784 \]
Thus,
\[ \text{Area of outer circle} = \frac{22}{7} \times 784 \]

### Step 2: Calculate the area of the inner circle
Similarly, for the inner circle with a radius of 21 m:
\[ \text{Area of inner circle} = \pi (21)^2 = \frac{22}{7} \times 21^2 \]
Calculating \( 21^2 \):
\[ 21^2 = 441 \]
Thus,
\[ \text{Area of inner circle} = \frac{22}{7} \times 441 \]

### Step 3: Calculate the area of the graveling
The area of the graveling is the area of the outer circle minus the area of the inner circle:
\[ \text{Area of graveling} = \text{Area of outer circle} - \text{Area of inner circle} \]
Substituting the areas calculated:
\[ \text{Area of graveling} = \left(\frac{22}{7} \times 784\right) - \left(\frac{22}{7} \times 441\right) \]
Factoring out \( \frac{22}{7} \):
\[ \text{Area of graveling} = \frac{22}{7} \times (784 - 441) \]
Calculating \( 784 - 441 \):
\[ 784 - 441 = 343 \]
Thus,
\[ \text{Area of graveling} = \frac{22}{7} \times 343 \]

### Step 4: Calculate the area of graveling
Now, calculate \( \frac{22}{7} \times 343 \):
\[ \text{Area of graveling} = \frac{22 \times 343}{7} \]
Calculating \( 22 \times 343 \):
\[ 22 \times 343 = 7546 \]
Now divide by 7:
\[ \text{Area of graveling} = \frac{7546}{7} = 1078 \text{ m}^2 \]

### Step 5: Calculate the cost of graveling
The cost of graveling is given as Rs. 5 per square meter. Therefore, the total cost is:
\[ \text{Cost} = \text{Area of graveling} \times \text{Cost per sq m} \]
Substituting the values:
\[ \text{Cost} = 1078 \times 5 = 5390 \text{ Rs} \]

### Final Answer
The cost of graveling the track is **Rs. 5390**.

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