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If the radius of the sphere is increased by 100%,the volume of corresponding sphere is increased by 700% .Find true or false.Justify Your answer




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Sphere volume formula is 
V= \frac{4}{3} \pi r^3  

So V is directly proportional to CUBE of radius.
new radius is r + 100%r = r+r = 2r
and new Volume given is V+ 700%V = 8V

Now lets see if 2r gives volume 8V....

 \frac{V_1}{V_2} = \frac{r_1^3 }{r_2^3 } 

V_1 = V, r_1 = r, r_2 =2r 

 \frac{V}{V_2} = \frac{r^3}{(2r)^3 } =  \frac{r^3}{8r^3} =  \frac{1}{8}

So V2 = 8V as expected.
hence the statement is true :) 
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