Q16 of 51 Page 1

A shuttle cock used for playing badminton has a shape of a frustum of cone mounted on a hemisphere as shown in the figure. The diameters of the ends of the frustum are 5 cm and 2 cm, the height of the entire shuttle cock is 7 cm. Find the external surface area. (Take )

Given:


Radius of lower end “r” = = 1 cm


Radius of upper end “R” = = 2.5 cm


Height of frustum “H” = 6 cm


To find: The external surface area.


Formula Used:


CSA of frustum = π(R + r)L


CSA of hemisphere = 2πr2


Explanation:


Let “L“ be the slant height of the frustum,


L of frustum =






= 6.18 cm


External Surface Area = CSA of frustum + CSA of hemisphere


= π(R + r)L + 2πr2


= π [(2.5 + 1)6.18 + 2 (1)2] cm2


= [(3.5)6.18 + 2] cm2


= [ 21.63 + 2] cm2


= (23.63) cm2


= cm2


= 74.26 cm2


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