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Question
An oil funnel of the tin sheet consists of a cylindrical portion 10 cm long attached to a frustum of a cone. If the total height is 22 cm, the diameter of the cylindrical portion by 8 cm and the diameter of the top of the funnel be 18 cm, then find the area of the tin sheet required to make the funnel.
Solution
Total height of oil funnel = 22 cm
Height of the cylindrical portion = 10 cm
Height of the frustum (h) = 22 – 10 = 12 cm
Radius of the cylindrical portion = 4 cm
Radius of the bottom of the frustum = 4 cm
Top radius of the funnel (frustum) = `18/2` = 9 cm
Area of the tin sheet required = C.S.A of the frustum + C.S.A of the cylinder
= π (R + r) l + 2πrh sq.units.
= `[pi(9 + 4) sqrt(12^2 + (9 - 4)^2) + 2pi xx 4 xx 10]"cm"^2`
= `pi[13 xx sqrt(144 + 25) + 25 + 80]"cm"^2`
= `22/7 [13 xx 13 + 80] "cm"^2`
= `22/7 [169 + 80] "cm"^2`
= `22/7 xx 249 "cm"^2`
= 782.57 cm2
Area of sheet required to make the funnel = 782.57 cm2
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