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Question
The surface area of a solid metallic sphere is 616 cm2. It is melted and recast into smaller spheres of diameter 3.5 cm. How many such spheres can be obtained?
Solution
The surface area of sphere = 4πr2
4πr2 = 616
r2 = `(616 xx 7)/(4 xx 22)`
r = 49
r = `sqrt49`
r = 7 cm
Volume of big sphere = `4/3πr^3 = 4/3 xx 22/7 xx (7)^3`
Volume of small sphere = `4/3 π(3.5/2)^3`
∴ No of smaller sphere = `"Volume of big sphere"/"Volume of small sphere"`
= `(4/3π (7)^3)/(4/3π (3.5/2)^3)`
= 64.
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