Question 6 - Important Questions on Surface Area and Volume - Chapter 12 Class 10 Surface Areas and Volumes
Last updated at April 16, 2024 by Teachoo
Important Questions on Surface Area and Volume
Important Questions on Surface Area and Volume
Last updated at April 16, 2024 by Teachoo
Question 6 Derive the formula for the curved surface area and total surface area of the frustum of a cone, given to you in Section 13.5, using the symbols as explained. There are two cones OCD & OAB We are given Height of frustum = h Slant height of frustum = l Radius PB = r1 Radius QD = r2 We need to find Curved Surface Area & Total Surface Area Here, We need to write h1, l1, h2, l2 in terms of h and l Curved Surface area of frustum ABDC = Curved Surface area of cone OAB Curved Surface area of cone OCD = r1l1 r2l2 In OPB & OQD BOP = DOQ OPB = OQD So, OPB OQD / = / _1/ _2 = _1/ _2 Putting l1 = l + l2 _1/ _2 = ( + _2)/ _2 _1/ _2 = / _2 + _2/ _2 _1/ _2 = / _2 + 1 _1/ _2 1 = / _2 ( _1 _2)/ _2 = / _2 _2 (( _1 _2)/ _2 ) = _2 = ( _2/( _1 _2 )) From (1) Curved Surface area of frustum = r1l1 r2l2 Putting l1 = l + l2 = r1(l + l2) r2l2 From (2): Putting _2 = ( _2/( _1 _2 )) = r1(l + ( _2/( _1 _2 ))) r2 ( _2/( _1 _2 )) = r1l (1 + ( _2/( _1 _2 ))) r2 ( _2/( _1 _2 )) = r1l (( _1 _2 + _2)/( _1 _2 )) r2 ( _2/( _1 _2 )) = r1l ( _1/( _1 _2 )) r2 ( _2/( _1 _2 )) = l ( _1 ^2/( _1 _2 )) ( _2 ^2/( _1 _2 )) = l (( _1 ^2 _2 ^2)/( _1 _2 )) = l ((( _1 _2)( _1+ _2))/( _1 _2 )) = l( _1+ _2) = ( _1+ _2 ) Curved Surface area of frustum = ( _ + _ ) Total Surface area of frustum = Curved Surface area of frustum + Area of top circle + Area of bottom circle = ( _1+ _2 ) + _1 ^2 + _2 ^2 Total Surface area of frustum = ( _ + _ ) + _ ^ + _ ^