Question

If the radius of sphere is 10cm if it is increased by 1cm. Then find the volume of the sphere increased by? ​

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%

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%.