A solid metallic sphere of diameter 28cm is melted and recasted into a no. of smaller cones, each of diameter 42/3 cm and height 3 cm. find the nos. of wires so formed.
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Well, when the metallic sphere is melted and recast into cones, wires cannot be formed. So, in reality, there are no wires made from the recast metallic sphere.
On the other hand, if you want to find the number of cones, then it can be found out by dividing the volumes of the sphere and one cone.
Volume of sphere = pi * 14*14*14 (where r = 14 = 28/2)
Volume of cone = 1/3 * pi * 14/6 * 14/6 * 3
Therefore number of cones = (pi * 14*14*14) / (1/3 * pi * 14 * 14 * 3 / 36)
= 36 * (pi * 14 * 14 * 14) / (pi * 14 * 14) = 36 * 14 = 504 cones.
There are no wires, but 504 cones.
On the other hand, if you want to find the number of cones, then it can be found out by dividing the volumes of the sphere and one cone.
Volume of sphere = pi * 14*14*14 (where r = 14 = 28/2)
Volume of cone = 1/3 * pi * 14/6 * 14/6 * 3
Therefore number of cones = (pi * 14*14*14) / (1/3 * pi * 14 * 14 * 3 / 36)
= 36 * (pi * 14 * 14 * 14) / (pi * 14 * 14) = 36 * 14 = 504 cones.
There are no wires, but 504 cones.
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