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Example – 6. A conical tent is to accommodate 11 persons. Each person must have 4 sq. metres of the space on the ground and 20 cubic metres of air to breathe. Find the height of the cone.

Solution :- Area of the base of the cone = πr² = 11 × 4

Or,  (22/7) r² = 44

Or,   r² = (44)(7/22)
                        = 14

Volume of the tent = (1/3)πr²h = 11×20

(1/3)(22/7)(14)h = 220

h = (220)(3)(7/22)(1/14)

   = 15 m.

Example – 7. A semi-circular thin sheet of metal of diameter 28 cm is bent and an open conical cup is made. Find the capacity of the cup. (Use π = 22/7).

Solution :- Slant height of the conical cup, l = Radius of the semi-circular sheet, R = 14 cm.

Let radius and height of the conical cup be r and h respectively.

Circumference of the base of the cone = Length of arc of semi-circle

Or, 2πr = (1/2)2πR

Or, 2πr = (1/2)(2π)(14)

Or, r = 7 cm
              l² = r² + h²
              (14)² = (7)² + h²

Or, h² =   (14)² – (7)²

Or, h  = 14

Or, h = √(147)

Or, = 12.124 cm

Volume of the conical cup = (1/3)πr²h = (1/3)(3.14)(7)²(12.124)

= 621.76421 = 622 cm³.