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Mathematics

Surface area of a solid

A solid metal...

Question

A solid metal sphere of surface area $S_{1}$ is melted and recast into a number of smaller spheres. $S_{2}$ is the sum of the surface areas of all the smaller spheres. Then

$S_{1} > S_{1}$

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$S_{2} > S_{1}$

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$S_{1} = S_{2}$

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$S_{1} = S_{2}$ only if all the smaller spheres are of equal radii.

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Solution

The correct option is B
$S_{2} > S_{1}$

Total surface area of all spheres always increases when a solid metal sphere is melted and recast into a number of smaller spheres.

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A solid metal sphere of surface area S1 is melted and recast into a number of smaller spheres. S2 is the sum of the surface areas of all the smaller spheres. Then

The correct option is B S2>S1 Total surface area of all spheres always increases when a solid metal sphere is melted and recast into a number of smaller spheres.

A solid metal sphere of surface area $S_{1}$ is melted and recast into a number of smaller spheres. $S_{2}$ is the sum of the surface areas of all the smaller spheres. Then

The correct option is B
$S_{2} > S_{1}$

Total surface area of all spheres always increases when a solid metal sphere is melted and recast into a number of smaller spheres.