Question

the radius of a sphere is 10cm. if the radius is increased by 1cm. then prove that volume of the sphere is increased by 33.1 percent.
Answer - 51 percent

Answer 1

vol. of sphere =4/3 πr^3
r=10 cm
vol,v1= (4/3π)1000
when r is inc. by 1cm new radius =11
vol,v2=(4/3π)13331
now percent change =(v2-v1)/v1
=(331/1000) *100
=33.1%

hence proved

Answer 2

We know that Volume of the sphere = 4/3 pi r^3

Volume of the sphere when radius = 10cm

        4/3 * pi * (10)^3

 Given that radius is increased by 1cm = 11cm.

Volume of the sphere when radius = 11cm

       4/3 * pi * (11)^3.  (New volume)


Increase in volume = 4/3 * pi * (11)^3 - 4/3 * pi * (10)^3

                                 = 4/3 * pi * ((11)^3 - (10)^3).
  
                                  = 4/3 * pi * (1331 - 1000)

                                   = 4/3 * pi * 331

Increase % = Increase in volume/Initial volume * 100

                   = 4/3 * pi * 331/4/3 * pi * (10)^3 * 100

                   = 4/3 * 22/7 * 331 * 100

                   = 331/1000 * 100

                   = 33.1%.



Hope this helps!