Question

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 (see the given figure).

Answer 1

Radius (r₁) of upper circular end of frustum part  = 18/2 = 9 cm

Radius (r₂) of lower circular end of frustum part = Radius of circular end of cylindrical part

= 8/2 = 4 cm

Height (h₁) of frustum part = 22 − 10 = 12 cm

Height (h₂) of cylindrical part = 10 cm

Slant height (l) of frustum part  =

` sqrt(r_1-r_2^2+h_2) = sqrt((9-4)^2+(12)^2) = 13 cm`

Area of tin sheet required = CSA of frustum part + CSA of cylindrical part

`=pi(r_1+r_2)l+2pir_2h_2`

`=22/7xx(9+4)xx13+22/7xx4xx10`

`=22/7[169+80] = (22xx249)/7`

`=782 4/7 cm^2`