Question

If radius is increased by 400% then, volume of corresponding sphere is increased by _ %
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Answer 1

Answer:

it will increase by 20%

Answer 2

The percentage increase in volume of sphere is 124%

Step-by-step explanation:

Given as :

The initial radius of a sphere = r

The initial volume of sphere = v

The percentage increase in radius = 400%

So, Final radius of sphere = r + 400% of r

i.e                                      R = r + $\dfrac{400}{100}$ × r

Or,                                     R = r + 4 r

Or,                                     R = 5 r

∵  volume of sphere = $\dfrac{4}{3}$ × π × Radius³

So, volume of sphere for radius r

ie,                            v = $\dfrac{4}{3}$ × π × r³

Or,                          v = A r³                             ( let A = $\dfrac{4}{3}$ × π )

volume of sphere for radius

                               v' = $\dfrac{4}{3}$ × π × (R)³

i.e                             v' = $\dfrac{4}{3}$ × π × (5r)³

Or,                            v' = $\dfrac{4}{3}$ × π × 125 r³

Or,                           v' = 125 A r³

Now,

% increase in volume =  $\dfrac{v'-v}{v}$  × 100

Or, % increase in volume =  $\dfrac{125 Ar^{3} -Ar^{3} }{Ar^{3} }$  × 100

Taking  A r³  as common

i.e   % increase in volume = $\dfrac{125-1}{1}$ × 100

∴     % increase in volume = 12400

So, The percentage increase in volume of sphere is 124%

Hence, The percentage increase in volume of sphere is 124%  Answer