Question

if the radius of a sphere is increased by 10% prove that it's volume will be increased by 33.1%.

Answer 1

volume of sphere initially. 4/3π(r)^3
then after increasing 10 % radius
now new radius will be 110/100r I.e, 11/10r
new volume of sphere
4/3.π.(11/10r)^3
when dividing we get final increase
[4/3.π.(11/10r)^3] / [4/3π(r)^3]
1331/1000
hence the final increase is 331 units in 1000 units
then increase percentage is
331/1000*100 %
then it is 33.1 %
hence it is proved

Answer 2

Hey here your answer

Volume of sphere = 4/3πr³

New volume when radius is increased by 10%.

4/3π(1.1r)³

Old volume = 4/3πr³
So, percentage change in volume is

[4/3π(1.1r)³ - 4/3πr³]/4/3πr³

On solving we get,
[(1.1)³ - 1³]/1 * 100%

(1.331-1)*100% = 0.331*100%

33.1%


I hope it's help you mark brainiest my dear friend