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The radii of the internal and external surfaces of a metallic spherical shell are 3 cm and 5 cm respectively. It is melted and recast into a solid right circular cylinder of height 10 cm. Find the diameter of the base of the cylinder.

OR

A solid metallic sphere of diameter 21 cm is melted and recast into a number of smaller cones each of diameter 7 cm and height 3 cm. Find the number of cones so formed.

Asked by Topperlearning User 20th February 2014, 3:13 PM
Answered by Expert
Answer:

The volume of the metal in the metallic spherical shell

Let the diameter of the base of the cylinder be r cm.

Since the volume of the hollow spherical shell will be equal to the volume of the cylinder casted.

r = 7

Hence, the diameter of the base of the cylinder is 7 cm.

OR

Let n be the number of cones formed.

Volume of sphere = volume of n cones

4 over 3 cross times straight pi cross times 21 over 2 cross times 21 over 2 cross times 21 over 2 equals 1 third cross times straight pi cross times 7 over 2 cross times 7 over 2 cross times 3 cross times straight n

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Answered by Expert 20th February 2014, 5:13 PM
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