ICSE Class X Math 2015 Solved Paper

Question : 29 of 52

Marks: +1, -0

Two solid spheres of radii

2 {\cm}

and

4 {\cm}

are melted and recast into a cone of height

8 {\cm}

. Find the radius of the cone so formed.

Solution:

\;\;\text " Volume of two spheres = Volume of cone "\;

\;\;{4}/{3} π(2)^3+\;{4}/{3} π(4)^3=\;{1}/{3} π r^2 h

\;32+256=r^2 × 8

\;\;{288}/{8}=r^2

\;36=r^2

\;r=6 {\cm} .

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