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Question

A cylindrical bucket, 32cm high and with radius of base 18cm, 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.


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Solution

STEP 1 :To find the radius of the heap

Let Radius of cone=R

According to question

Volume of Cylindrical bucket =The volume of Conical heap

πr2h=13πR2Hπr2h=13πR2H182×32=13×R2×2410368=R2×8R2=103688R2=1296R=1296R=36cm

STEP 2 : To find out the Slant Height of the heap

Slant height is given by the formula :

l=H2+R2=242+362=576+1296=1872=1213cm

Hence,

Radius of the Conical heap=36cm

Slant height of the Conical heap=1213cm.


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