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Home » A cylindrical bucket, high and of radius of the base, 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 , find the radius and slant height of the heap.
A cylindrical bucket, 32cm high and 18cm of radius of the base, 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 24cm, find the radius and slant height of the heap.
CBSE | Class 10 | Exercise 16.1 | Maths | RD Sharma | Surface Areas And Volumes
A cylindrical bucket, 32cm high and 18cm of radius of the base, 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 24cm, find the radius and slant height of the heap.

It is given that,

Height of the cylindrical bucket =32cm

Radius of the cylindrical bucket =18cm

Height of conical heap =24cm

As we know that,

Volume of cylinder =\pi \times {{r}^{2}}\times h

And, volume of cone =1/3\pi \times {{r}^{2}}\times h

So, from the question

Volume of the conical heap = Volume of the cylindrical bucket

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

{{r}^{2}}={{18}^{2}}\times 4

r=18\times 2=36cm

Then,

Slant height of the conical heap (l) is given by

l=\sqrt{\left( {{h}^{2}}+{{r}^{2}} \right)}

l=\sqrt{\left( {{24}^{2}}+{{36}^{2}} \right)}=\sqrt{1872}

l=43.26cm

Therefore, the radius and slant height of the conical heap are 36cm and 43.26cm respectively.

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