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 : 32 of 52

Marks: +1, -0

the radius of the sphere.

Solution:

\;\; \text{ Let the radius of sphere } \; = r \; \text{cm}

\;\; \text{ Surface area of sphere } \; = 4 \pi r^2

\; = 2464 \; \text{cm}^2 \; \text{ (given) } \;

\; \Rightarrow \;\; r^2 = \frac{2464}{4\pi}

\; r^2 = \frac{2464 \times 7}{4 \times 22} = 196

\; r = 14 \; \text{cm} .

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