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  • 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 th

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.).

                                                  

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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 

Posted by

Devendra Khairwa

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