the number of cones recast. (Take \pi= 22/7)

ICSE Class X Math 2014 Solved Paper - Question 33

ICSE Class X Math 2014 Solved Paper

The surface area of a solid metallic sphere is $2464 {\cm}^2$ . It is melted and recast into solid right circular cones of radius $3.5 {\cm}$ and height $7 {\cm}$ . Calculate :

Question : 33 of 52

Marks: +1, -0

the number of cones recast. (Take

π=

22/7)

Solution:

Volume of sphere

=\;{4}/{3} π r^3=\;{4}/{3} π(14)^3

Volume of cone

=\;{1}/{3} π r^2 h

\;=\;{1}/{3} π(3.5)^2 × 7

No. of cones recast

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

\;=\;{\;{4 π}/{3}(14)^3}/{{1}/{3} π(3.5)^2 × 7}

\;=\;{4 × 14 × 14 × 14}/{3.5 × 3.5 × 7}

\;=\;{3200}/{25}=128 .

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