ICSE Guess > ICSE/ISC eBooks > Class X > Maths by Mr. M. P. Keshari

ICSE / ISC eBooks

Example – 3. What length of canvas 2  m width is required to make a conical tent of 12 m  diameter and whose slant height is 6.3 m? Also find the cost of the canvas at the rate of Rs.12.50 per metre. (Take π = 22/7).

Solution :- r = 12/2 = 6 m, l = 6.3 m

Curved surface area of the tent = πrl = (22/7)(6)(6.3)  = 118.8 m²

Length of the canvas = 118.8 ⁄ 2 = 59.4 m

Cost of the canvas = Rs.12.50 × 59.4 = Rs.742.50

Example – 4. A hollow cone 24 cm high with base radius 7 cm is made of the sheet of a metal. Find the area of the sheet of the metal required including the base. Also find the capacity of the cone.

Solution :-l² = r² + h²  = (7)² + (24)² = 625
                                             l = 25 cm

Total surface area of the cone = πr(r + l) = (22/7)(7)(7 + 25) = 704 cm².

Capacity of the cone = (1/3)πr²h = (1/3)(22/7)(7)²(24) = 1232 cm³.

Example 5. The radius and slant height of a cone are in the ratio of 4 : 7. If its curved surface area is 792 cm2, find its radius. (Use π = 22/7).

Solution :-  r : l  =  4 : 7

Let , r = 4x and l = 7x

Curved surface area = πrl = 792

Or,  (22/7)(4x)(7x) = 792

Or,  88x² = 792

Or,  x² = 9

Or,  x = 3

Thus, r = (4)(3) =  12 cm.