Question

if the radius of a sphere is increased 50% find increase volume in percent

Answer 1

Hope it will help you.Thank you

Answer 2

Answer:

237.5%.

Step-by-step explanation:

Let the radius be x

Volume of sphere = $\frac{4}{3} \pi r ^3$

Where r is the radius

So, radius of given sphere =  $\frac{4}{3} \pi x^3$

Now  radius of a sphere is increased 50%

So, New radius = $\frac{50}{100}x+x =\frac{150x}{100}$

So, New Volume =  $\frac{4}{3} \pi (\frac{150x}{100})^3$

                          =  $\frac{4}{3} \pi (\frac{3x}{2})^3$

                          =  $\frac{9}{2} \pi x^3$

Change in volume = New volume - Original volume

                             =  $\frac{9}{2} \pi x^3-\frac{4}{3} \pi x ^3$

                             =  $\frac{19}{6} \pi x^3$

So, Increase in volume in percent =$\frac{\text{Change in volume}}{\text{original volume}} \times 100$

                                                         =$\frac{frac{19}{6} \pi x^3}{\frac{4}{3} \pi x ^3} \times 100$

                                                         =$237.5\%$

Hence increase volume in percent  is 237.5%.