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  • A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap.

7. A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap.

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According to question volume will remain constant thus we can write :

The volume of bucket    =    Volume of heap formed.

                  \pi r^2_1h_1\ =\ \frac{1}{3}\pi r^2_2 h_2      

Let the radius of heap be r.

  \pi\times 18^2 \times 32\ =\ \frac{1}{3}\times \pi \times r^2\times 24

 r\ =\ 18\times 2\ =\ 36\ cm

And thus the slant height will be         

 l\ =\ \sqrt{r^2\ +\ h^2}

     =\ \sqrt{36^2\ +\ 24^2}

     =\ 12\sqrt{13}\ cm

Hence the radius of heap made is 36 cm and its slant height is  12\sqrt{13}\ cm.

Posted by

Devendra Khairwa

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