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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?
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Solution
The surface area of a sphere = 4πr2
4πr2 = 616
r2 = `(616 xx 7)/(4 xx 22)`
r2 = 49
r = `sqrt49`
r = 7 cm
Radius of a small sphere `(r_s) = 3.5/2`
= 1.75 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 spheres = `"Volume of big sphere"/"Volume of small sphere"`
= `(4/3π (7)^3)/(4/3π (3.5/2)^3)`
= 64
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