# 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 the diameter of the top of the funnel is 18 cm, find the area of the tin sheet required to make the funnel (see Fig.).

From this, we can write the values of both the radius (upper and lower) and height of frustum.

Thus slant height of frustum is :

$=\ \sqrt{\left ( r_1\ -\ r_2 \right )^2\ +\ h^2}$

$=\ \sqrt{\left ( 9\ -\ 4 \right )^2\ +\ 12^2}$

$=\ 13\ cm$

Now, the area of the tin shed required :

=  Area of frustum  +  Area of the cylinder

$=\ \pi \left ( r_1\ +\ r_2 \right )l\ +\ 2\pi r_2h$

$=\ \pi \left ( 9\ +\ 4 \right )13\ +\ 2\pi \times 4\times 10$

$=\ 782.57\ cm^2$

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