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# A cylindrical bucket, 32 cm high and 18 cm 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 24 cm, find the radius and slant height of the heap.

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In this question we have to find the radius and slant height of the heap given that a cylindrical bucket,
32 cm high and 18 cm 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 24 cm.

This question is from r d sharma class 10 maths.
I found this question while doing maths class 10. I need help in getting the solution.

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1. Given,

Height of the cylindrical bucket = 32 cm

Radius of the cylindrical bucket = 18 cm

Height of conical heap = 24 cm

We know that,

Volume of cylinder = π × r2 × h

And, volume of cone = 1/3 π × r2 × h

Then, from the question

Volume of the conical heap = Volume of the cylindrical bucket

1/3 π × r2 × 24 = π × 182 × 32

r2 = 182 x 4

r = 18 x 2 = 36 cm

Now,

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

l = √(h2 + r2)

l = √(242 + 362) = √1872

l = 43.26 cm

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

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