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, then find the area of the tin sheet required to make the funnel.

Answer 1

We have, 

Height of the cylindrical portion, h = 10 cm,

height of the frustum of cone portion, H = 22 - 10 = 12 cm,

Radius of the  cylindrical portion = Radius of smaller end of frustum portion,

Radius of larger end of frustum portion, R = 18/2 = 9 cm

Also, the slant height of the frustum, `l = sqrt(("R - r")^2 + "H"^2)`

`=sqrt((9 - 4)^2+12^2`

`=sqrt(5^2+12^2)`

`=sqrt(25+144`

`=sqrt(169)`

`=13  "cm"`

Now,

The area of the tin sheet required = CSA of frustum of cone + CSAA of cylinder

= π (R + r) l + 2πrh

`= 22/7xx(9+4)x13+2xx22/7xx4xx10`

`=22/7xx13xx13+22/7xx80`

`= 22/7xx(169+80)`

`=22/7xx249`

≈ 782.57 cm² 

So, the area of the tin sheet required to make the funnel is 782.57 cm².