Q. 74.1( 203 Votes )

# 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

Answer :

Given:

Height (*h _{1}*) of cylindrical bucket = 32 cm

Radius (*r _{1}*) of circular end of bucket = 18 cm

Height (*h _{2}*) of conical heap = 24 cm

Let the radius of the circular end of conical heap be *r _{2}*

The volume of sand in the cylindrical bucket will be equal to the volume of sand in the conical heap

Volume of sand in the cylindrical bucket = Volume of sand in conical heap

π r_{1}^{2} x h_{1} = 1/3 π x r_{2}^{2} x h_{2}

π x (18)^{2} x 32 = 1/3 x π x r_{2}^{2} x 24

= 36 cm

l = 12 cm

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