Question

the radius of a sphere is increased by 10%. prove that the volume is increased by 33.1%

Answer 1

let radius of sphere =100 unit

volume of sphere =4/3pi (100)^3

=4/3 pi.1000000cube unit

now increase 10% in radius

radius=100 +10% of 100

=100 +10 x 100/100=110 unit

volume of sphere =4/3 pi (110)^3

=4/3pi. (1331000) cube unit

% increase in volume ={4/3pi. (1331000-1000000)/4/3pi.1000000} x 100

={331000/1000000} x 100

=33.1 %