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Example 1. A right circular cone has base radius 6 cm and height 8 cm. Find the following :

1. the slant height of the cone;
2. the surface area of the cone;
3. the total surface area of the cone;
4. the volume of the cone.

Solution :-

fig. – 3 .

(i)   Here, slant height, l = ?, radius, r = 6 cm, height, h = 8 cm. 
                       l² = r² + h² = 6² + 8² = 36 + 64 = 100
                        l = √100 = 10 cm.  
(ii) Surface area of the cone = πrl = (22/7)(6)(10) = 188.5 cm².
(iii) Total surface area of the cone = πr(r + l) = (22/7)(6)(6 + 10) = 301.6 cm².  
(iv) Volume of the cone = (1/3) πr2h = (1/3)(22/7)(6)²(8) = 301.6 cm³.

Example 2. A conical tent has the area of its base as 154 m² and that of its curved surface as 550 m². find the volume of the tent.(Use π = 22/7).

Solution :- Area of the base = πr² = 154

                     Or, (22/7)r²  =  154
                     Or,           r²  =  (154)(7/22)  =  49
                     Or,           r    =   7 m.
                   Curved surface area = πrl = 550
                      Or, (22/7)(7)l  =  550
                      Or,                l  =  550/22  =  25 m
                                    l² = r² + h²
                               (25)2 = (7)² + h²2
                              Or, h2 = (25)² – (7)² = 576
                              Or, h = 24 m

Volume of the cone = (1/3)πr²h =  (1/3)(22/7)(7)²(24) 1232 m³.