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5 persons will live in a tent. If each person requires 16 m² of floor area and 100 m³ space for air then the height of the cone of smallest size to accommodate these persons would be
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- 16 metre
- 10.25 metre
- 20 metre
- 18.75 metre
- 16 metre
Correct Option: D
Let the radius of the base of conical tent be r metre and its height be h metre.
∴ Area of base = πr² = 16 × 5 = 80 ......(i)
| Volume = | πr²h | |
| 3 |
= 5 × 100 cu. metre ......(ii)
On dividing equation (ii) by (i),
| = | = | |||
| 3 | πr² | 80 |
| ⇒ h = | = 18.75 metre | |
| 4 |
