Question

A+solid+spherical+ball+of+radius+6cm+is+melted+and+recast+into+64+identical+spherical+marbles.+Find+the+radius+of+each+marble

Answer 1

Answer:

volume of spherical ball = volume of 64 spherical marbles

---> 4/3πR³=64×4/3πr³

---> R³=64×r³

---> (6)³=64×r³

---> 216=64×r3

---> 216/64=r3

--->27/8=r3

r=√27/2

Answer 2

Radius of each marble = 1.5 cm

Given:

Solid sphere of ball 6 cm.

Recast into 64 identical spherical marbles.

To find:

radius of each marble.

Formula used:

Volume of sphere = $\frac{4}{3}$ × $\pi$ ×(Radius)³

Explanation:

As the solid sphere is melted and form 64 identical spherical marbles.

Then the volume of solid sphere and 64 marbles are same.

Volume of sphere =  volume of 64 marbles

    $\frac{4}{3}$ × $\pi$ ×(Radius)³ =   64 × $\frac{4}{3}$ × $\pi$ ×(Radius)³

              $\frac{4}{3}$ × $\pi$ ×(6)³ = 64 × $\frac{4}{3}$ × $\pi$ ×(Radius)³

                           $\frac{6^{3} }{64}$ = (Radius)³

                           $\frac{216}{64}$ = (Radius)³

                    Radius = 1.5 cm.

Radius of each marble =1.5 cm

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