Question

Question 5
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 diameter of the top of the funnel is 18 cm, find the area of the tin sheet required to make the funnel.

Answer 1

Curved surface area of cylinder:
$=2\pi rh$
$=\pi \times 8\times 10$
$=80\pi$
Slant height of frustum can be calculated as follows:
$l=\sqrt{h^2+(r_1-r_2{)}^2}$
$=\sqrt{{12}^2+(9-4{)}^2}$
$=\sqrt{144+25}$
$=\sqrt{169}=13cm$
Curved surface area of frustum:
$=\pi (r_1+r_2)l$
$=\pi (9+4)\times 13$
$=169\pi$
Total curved surface area:
$=169\pi +80\pi$
$=249+3.14$
$=781.86c{m}^2$