Q10 of 44 Page 15

An oil funnel of tin sheet consists of a cylindrical portion 8 cm along attached to a frustum of a cone. If the total height be 15cm, the diameter of the cylindrical portion 1 cm and diameter of the top of the funnel 10cm, find the area of the tin required. [Take π=22/7]


Diameter of top of funnel = 10cm


So, Radius (R) = 5cm


Diameter of cylindrical portion = 1cm


So,


Height of frustum = Total height – Height of cylindrical part


= 15 – 8


= 7cm


and Slant Height, l = √{h2 + (R – r)2}


= √{(7)2 +(5 – 0.5)2


= √49 + (4.5)2


= √49 + 20.25


= √69.25


= 8.32 cm


Now, CSA of frustum = πl (R + r)




= 143.81 cm2


Height of cylinder, H = 8cm


Now, CSA of cylinder = 2πrH



= 25.14 cm2


Area of tin required = CSA of frustum + CSA of cylinder


= 143.81 + 25.14


= 168.95 cm2


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