ICSE Class X Math 2016 Solved Paper

Question : 7 of 57

Marks: +1, -0

A certain number of metallic cones, each of radius

2 {\cm}

and height

3 {\cm}

are melted and recast into a solid sphere of radius

6 {\cm}

. Find the number of cones.

Solution:

\;\;\text " Let number of cones "\;=n

Volume of cones

=

Volume of sphere

= \;{1}/{3} π r^2 h × n\;=\;{4}/{3} π r^3

n × \;{1}/{3} π × 2^2 × 3\;=\;{4}/{3} π × 6^3

n\;=\;{216}/{3}

n\;=72

Hence, no. of cones

=72

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