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Question
Sand from a cylindrical bucket 32 cm in height and 18 cm in radius is poured onto the ground making a conical heap 24 cm high. Find the radius of the conical heap.
Solution
Height of the cylinder = h1 = 32 cm
Radius of bucket = r1 = 18 cm
Height of conical heap = h2 = 24 cm
Let radius of conical heap = r2
Volume of sand in the bucket = volume of sand in conical heap
⇒ `pi xx r1^2 xx h1 = 1/3 xx pi xx r2^2 xx h2`
⇒ `18 xx 18 xx 32 = 1/3 xx r2^2 xx 24`
⇒ `r2^2 = (10368 xx 3)/24`
⇒ `r2^2 = 1296`
⇒r2 = 36 cm
Radius of the conical heap = 36 cm
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