A conical tent is 7 m high and the radius of its base is 24 m.
(i) What is the cost of the canvas required to make it, if a square metre canvas costs Rs 20 ?
(ii) How many persons can be accommodated in the tent, if each person requires 5 square metre on the ground and `20 m^3` of space to breathe in?

Options

A. `{:((i),"(ii)"),(Rs 56521.30 ,190):}`
B. `{:((i),"(ii)"),(Rs 1456.20 ,292):}`
C. `{:((i),"(ii)"),(Rs 35625.48,362):}`
D. None of these

Answer

To solve the problem step by step, we will break it down into two parts as given in the question.

### Part (i): Cost of the canvas required to make the conical tent

1. **Identify the dimensions of the cone:**
- Height (h) = 7 m
- Radius (r) = 24 m

2. **Calculate the slant height (l) of the cone using the Pythagorean theorem:**
\[ l = \sqrt{r^2 + h^2} = \sqrt{24^2 + 7^2} = \sqrt{576 + 49} = \sqrt{625} = 25 \text{ m} \]

3. **Calculate the curved surface area (CSA) of the cone:**
\[ \text{CSA} = \pi r l = \frac{22}{7} \times 24 \times 25 \]
\[ = \frac{22 \times 24 \times 25}{7} = \frac{13200}{7} \approx 1885.71 \text{ m}^2 \]

4. **Calculate the cost of the canvas:**
- Cost per square meter = Rs 20
\[ \text{Total Cost} = \text{CSA} \times \text{Cost per square meter} = 1885.71 \times 20 = 37714.28 \text{ Rs} \]

### Part (ii): Number of persons that can be accommodated in the tent

1. **Calculate the area of the base of the cone:**
\[ \text{Area of base} = \pi r^2 = \frac{22}{7} \times 24^2 = \frac{22}{7} \times 576 = \frac{12672}{7} \approx 1810.29 \text{ m}^2 \]

2. **Calculate the number of persons that can stand in the tent:**
- Area required per person = 5 m²
\[ \text{Number of persons (area)} = \frac{\text{Area of base}}{\text{Area required per person}} = \frac{1810.29}{5} \approx 362.06 \text{ persons} \]

3. **Calculate the volume of the cone:**
\[ \text{Volume} = \frac{1}{3} \pi r^2 h = \frac{1}{3} \times \frac{22}{7} \times 24^2 \times 7 = \frac{22 \times 576}{3} = 4224 \text{ m}^3 \]

4. **Calculate the number of persons that can breathe in the tent:**
- Volume required per person = 20 m³
\[ \text{Number of persons (volume)} = \frac{\text{Total volume}}{\text{Volume required per person}} = \frac{4224}{20} = 211.2 \text{ persons} \]

5. **Determine the limiting factor:**
- The number of persons that can stand is approximately 362.
- The number of persons that can breathe is approximately 211.
- Therefore, the number of persons that can be accommodated in the tent is limited by the breathing space:
\[ \text{Number of persons accommodated} = 211 \]

### Final Answers:
- (i) The cost of the canvas required to make the tent is Rs 37714.28.
- (ii) The number of persons that can be accommodated in the tent is 211.