Question

The radius of a sphere is increased by 10%. Prove that the volume will be increased by 33% approximately

Answer 1

Let radius of sphere be 100 cm

New Radius = 100 + 10/100 * 100 = 110 cm

Original volume = 4 / 3 * pie * (100)3 ----- (i)

Volume with new radius = 4 / 3 * pie * (110)3 -------- (ii)

(ii) - (i)

Change in percent = [4 / 3 * pie * (110)3 - 4/ 3 * pie * (100)3 / 4 / 3 * pie * (100)3] * 100

= [(110)3 - (100)3 / (100)3]   *100

= [(11/10)3 - 1)] * 100

=( 1331 / 1000 - 1) *100

= (331 / 1000) * 100

= 33.1% approx.

Hence Proved

Answer 2

Here is your answer.......

Let the radius at initial case be 'r'
then the radius at increased state will be = r + r/10 = 11r/10

Volume in 1st case V1 = 4/3 πr³
Volume in 2nd case V2= 4/3 π(11r/10)³

∴ V2 - V1= [4/3 π(11r/10)³] - [4/3 πr³] = 4/3π[1331-100)r/100]³               = 4/3π * 331r³/1000


Therefore %age increase = V2-V1 / V1 * 100
                                         =  (4/3π * 331r³/1000) / 4/3πr³
                                         = 331/100 = 33.1% 


  So, approx increased vol = 33.1% ≈ 33%

I hope it helps you ^_^