NIFT UG 2019 Question Paper with solutions

Question : 18 of 150

Marks: +1, -0

A solid sphere of

6 {cm}

diameter is melted and recast into 8 solid spheres of equal volume. The radius (in

{cm}

) of each small sphere is

Solution:

Volume of solid sphere

=\;{4}/{3} π r^{3}=\;{4}/{3} π × 3 × 3 × 3

=36 π {cu} {cm}

Let the radius of small sphere be

x

.
Then, according to the question,
Volume of sphere

=8 ×

Volume of small sphere

⇒ \;\; 36 π =8 × \;{4}/{3} π x^{3}

⇒ \;\; x^{3}=\;{36 × 3 × π}/{8 × 4 × π}

=\;{9 × 3}/{8}

x=\;{3}/{2}=1.5 {cm}

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