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Question

504 cones, each of diameter 3.5cm and height 3cm, are melted and recast into a metallic sphere. Find the diameter of the sphere.


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Solution

Step1 : Find Volume of 504 cones

Given,

Diameter of each cone =3.5cm

Radius, r=3.52

Height of each cone =3cm

Thus the volume of each cone, V=13πr2h

=13π(3.52)2×2.3

=13×227×3.52×3.52×3

=19.252cm3

Thus, volume of 504 cones =504×19.252=4851cm3

Step 2: Find the diameter of the sphere

As per the given condition, 504 cones are melted to form a sphere. Thus, the volume of 504 cones and sphere made from them will be the same.

Hence,

Volume of sphere =4851cm3

43×π×r3=4851

r3=4851×34×π

r=10.5cm

Therefore, the diameter of the sphere is, d=2x10.5=21cm.


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