Question

answer fastly it was important

Answer 1

I think ur answer is 88 cm....

Answer 2

Solution:

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Given:


The ratio of the volume of two spheres = 64 : 27


Let the ratio be in the form of r,.


$\frac{64}{27} = \frac{ \frac{4}{3} \pi R^3 }{ \frac{4}{3} \pi r^3 }$


$\frac{64}{27} = \frac{R^3}{r^3}$


$( \frac{4}{3})^3 = ( \frac{R}{r})^3$


$\frac{4}{3} = \frac{R}{r}$ ..(i)


The sum of their radius = 7,.


R + r =7,. (ii)


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To find :


Difference in their surface area,.


4πR²-4πr² = ?


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As we know,.


R + r = 7,.


        R = 7 - r ...(iii)


(i)=>$\frac{4}{3} = \frac{R}{r}$



=>$\frac{4}{3} = \frac{7-r}{r}$



=> 4r = 3(7-r)


=> 4r =21- 3r


=> 4r + 3r = 21


=> 7r = 21


=> r = 3cm


∴ Radius of smaller sphere is 3 cm.


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(iii)=> R = 7- r


=> R = 7 - 3


=> R = 4cm,.


       ∴ Radius of larger circle is 4 cm.


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The difference in their surface area is,


=> 4πR²-4πr²


=> 4π(R²-r²)


=> 4π(R+r)(R-r)


substituting the values,.


=> $4( \frac{22}{7}) (4+3)(4-3)$


=>$4( \frac{22}{7} ) (7)(1)$


=> 4(22)


=> 88cm²


       ∴ The difference in the surface area of the given two spheres are 88cm²

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                                          Hope it Helps !!