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Maths-

General

Easy

Question

Twenty seven solid iron spheres , each of radius r and surface area S are melted to form a sphere with surface area S’. Find the i) Radius r’ of the new sphere ii) ratio of S and S’

hint Hint:

The surface area of a sphere is $4 pi r squared$

The correct answer is: 1:9

Explanation:

We have given twenty seven solid iron spheres , each of radius r and surface area S are melted to form a sphere with surface area S’.

We have to find the Radius of new sphere and the ratio of S and S’

Step 1 of 2:
We have given 27 solid spheres each of radius r and surface area s
So,
(i)
Volume of each sphere will be
$V equals 27 cross times 4 over 3 pi r cubed$
Volume of big sphere
$V equals 4 over 3 pi r to the power of 13$
So,
$4 over 3 pi r to the power of straight prime 3 end exponent equals 27 cross times 4 over 3 pi r cubed$
$r to the power of straight prime equals 3 r$
Step 2 of 2:
Surface area is $4 pi r squared$
$s equals 4 pi r squared$ and
$equals 4 pi left parenthesis 3 r right parenthesis squared$
$equals 36 pi r squared$
Therefore,
$s over s to the power of straight prime equals fraction numerator 4 pi r squared over denominator 36 pi r squared end fraction$
= $1 over 9$
Or
1 : 9

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