Question

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

Answer 1

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

So V is directly proportional to CUBE of radius.
so,
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....

[tex] \frac{V_1}{V_2} = \frac{r_1^3 }{r_2^3 } V_1 = V, r_1 = r, r_2 =2r [/tex]

[tex] \frac{V}{V_2} = \frac{r^3}{(2r)^3 } = \frac{r^3}{8r^3} = \frac{1}{8} [/tex]

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

Answer 2

Answer: The statement is true

Step-by-step explanation:

Volume of sphere=4/3πr^3

When radius is increased by 100% then r= r+100%r

= r+r =2r

New volume = (2r) ^3

= 8r^3

So therefore when radius is increased by 100% the volume will increase by 800%