An oil funnel made of tin sheet consists of a 10 cm long cylindrical portion attached to a frustum of a cone. If the total height is 22 cm , diameter of the cylindrical portion is 8 cm and the diameter of the top of the funnel is 18 cm, find the area of the tin sheet required to make the funnel.
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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]
Class 10th
KC Sinha - Mathematics
14. Surface Areas and Volumes
Answer
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