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Question

A girl fills a cylindrical bucket whose height is 32 cm and radius is 18 cm with sand. She empties the bucket on the ground and makes a conical heap of the sand. If the height of the conical heap is 24 cm, then the slant height of the cone formed is:

A

1312 cm

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B

1213 cm

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C

626 cm

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D

127 cm

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Solution

The correct option is B

1213 cm


Given, radius of cylindrical bucket = r1 = 18 cm
Height of cylindrical bucket = h1 = 32 cm
Radius of conical heap = r2
Height of the conical heap = h2 = 24 cm

According to questions,
Volume of cylinder = Volume of conical heap
πr21h1=13πr22h2r21h1=13r22h218×18×32=13×r22×24r22=18×18×4r2=36 cm
Radius of the iconical heap = 36 cm

Now, slant height of conical heap,
l=r22+h22=(36)2+(24)2=1296+576=1872=1213 cm


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