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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.
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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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