NumericalModerate3 marks
A conical tent is to accommodate 77 persons. Each person must have 16 m³ of air to breathe. Given the radius of the tent as 7 m, find the height of the tent and also its curved surface area
Topic: Mensuration of solids
Previous-year question practice database
Answer
Exam answer
Total air needed = 77 × 16 = 1232 m³.
For a conical tent: V = (1/3)πr²h.
1232 = (1/3) × 22/7 × 7² × h = (154/3)h.
h = 24 m.
Slant height: l = √(7² + 24²) = 25 m.
Curved surface area: πrl = 22/7 × 7 × 25 = 550 m².
Answer: Height = 24 m; Curved surface area = 550 m².
Explanation
Use the total air requirement as the cone volume. Then calculate slant height by Pythagoras and use Curved surface area = πrl.
More from Cylinder, Cone and Sphere
The total surface area of a solid sphere (S1) and a solid hemisphere (S2), as shown in the diagram, are equal. The ratio of radii R and r is :2026minimum height of the cylindrical box required to pack this bottle.2026volume of the liquid medicine (shaded part) in the bottle. Give your answer to the nearest whole number. (Use π = 22/7 )2026the total surface area of the given solid.2026the cost of painting the total surface at the rate of ₹0.50 per cm.2026If the volume of two spheres is in the ratio 27: 64, then the ratio of their radii is:2025