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

ICSE Class X Math 2014 Paper

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

Question : 33 of 52

Marks: +1, -0

the number of cones recast. (Take

\pi =

22/7)

Solution:

Volume of sphere

= \frac{4}{3} \pi r^3 = \frac{4}{3} \pi (14)^3

Volume of cone

= \frac{1}{3} \pi r^2 h

= \frac{1}{3} \pi (3.5)^2 \times 7

No. of cones recast

= \frac{ \text{Volume of sphere} }{ \text{Volume of cone} }

= \frac{ \frac{4\pi}{3} (14)^3 }{ \frac{1}{3}\pi (3.5)^2 \times 7 }

= \frac{4 \times 14 \times 14 \times 14}{3.5 \times 3.5 \times 7}

= \frac{3200}{25} = 128.

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