ICSE Class X Math 2013 Solved Paper

Question : 33 of 46

Marks: +1, -0

A solid sphere of radius

15 {\cm}

is melted and recast into solid right circular cones of radius

2.5 {\cm}

and height

8 {\cm}

. Calculate the number of cones recast.

Solution:

Radius of a solid sphere,

r=15 {\cm}

\;\text " Volume of a solid sphere "\;\;=\;{4}/{3} π r^3

\;=\;{4}/{3} × π(15)^3 {\cm}^3 .

Now, radius of right circular cone

=2.5 {\cm}

and

\;\text " height, "\; h=8 {\cm} \;\text ". "\;

Volume of right circular cone

=\;{1}/{3} π r^2 h

=\;{1}/{3} π(2. 5)^2 × 8

∴

The number of cones

=\;{\;\text " Volume of a sphere "\;}/{\;\text " Volume of a cone "\;}

\;=\;{\;{4}/{3} π ×(15)^3}/{{1}/{3} π(2.5)^2 × 8}

\;=\;{15 × 15 × 15}/{2.5 × 2.5 × 2}

\;=270

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