The inner and outer radii of a circular track area respectively 21 m and 28 m. The cost of levelling the track at ₹ 5 per sq m is

Options

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

Answer

To solve the problem of finding the cost of leveling a circular track with given inner and outer radii, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values:**
- Inner radius (r1) = 21 m
- Outer radius (r2) = 28 m
- Cost of leveling per square meter = ₹ 5

2. **Calculate the area of the outer circle (A_outer):**
\[ A_{\text{outer}} = \pi r_2^2 = \pi (28)^2 = \pi \times 784 \]

3. **Calculate the area of the inner circle (A_inner):**
\[ A_{\text{inner}} = \pi r_1^2 = \pi (21)^2 = \pi \times 441 \]

4. **Find the area of the track (A_track):**
\[ A_{\text{track}} = A_{\text{outer}} - A_{\text{inner}} = \pi \times 784 - \pi \times 441 = \pi (784 - 441) = \pi \times 343 \]

5. **Calculate the area of the track in terms of π:**
\[ A_{\text{track}} = 343\pi \text{ square meters} \]

6. **Calculate the cost of leveling the track:**
\[ \text{Cost} = \text{Area} \times \text{Cost per square meter} = 343\pi \times 5 \]

7. **Substitute the value of π (using \(\frac{22}{7}\) for approximation):**
\[ \text{Cost} = 343 \times \frac{22}{7} \times 5 \]

8. **Simplify the expression:**
\[ \text{Cost} = 343 \times 22 \times \frac{5}{7} = 343 \times 22 \times \frac{5}{7} = 343 \times 22 \times 0.7142857 \]
\[ = 343 \times 22 \times 5 / 7 = 343 \times 110 / 7 = 3430 \]
\[ = 343 \times 22 = 7556 \]
\[ = 343 \times 5 = 1715 \]
\[ = 1715 \times 22 = 37730 \]

9. **Final Calculation:**
\[ \text{Cost} = 343 \times 22 \times 5 = 343 \times 110 = 37730 \]

### Final Answer:
The cost of leveling the track is ₹ 5390.