Q. 133.9( 8 Votes )

# A cylindrical bucket of height 32 cm and base radius 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.

Answer :

For cylindrical bucket,

Radius, r = 18 cm

Height, h = 32 cm

As we know,

Volume of cylinder = πr^{2}h

Where r is base radius and h is height of cylinder.

Volume of sand in bucket = π(18)^{2}(32) cm^{3}

Also, For conical heap

Let the radius be r and height, h = 24 cm is given,

As we know,

Where r is base radius and h is height of cone

As the volume of sand is constant

Volume of sand in bucket = Volume of conical heap

π (18)^{2}(32) = 8πr^{2}

(18)(18)(4) = r^{2}

r = 18(2) = 36 cm

Also, we know

l^{2} = h^{2} + r^{2}, where h , r and l are height radius respectively.

l^{2} = (24)^{2} + (36)^{2} = 576 + 1296 = 1876

l = 43.267 cm

So, radius and slant height of heap are 36 cm and 43.267 cm respectively.

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