Question

The radius of the sphere is increased by 10% and prove that the volume is increased by 33.1 % approximately

Answer 1

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Radius of sphere be 100 cm

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

Original volume = 4 / 3 x 22/7 x (100)3 ----- (i)

Volume with new radius = 4 / 3 x 22/7 x (110)3 -------- (ii)

from (ii) & (i)

Change in percent

=> [4 / 3 x 22/7 x (110)3 - 4/ 3 x 22/7 x (100)3 / 4 / 3 x 22/7 (100)3] x 100

= [(110)3 - (100)3 / (100)3]   x 100

= [(11/10)3 - 1)] x 100

=( 1331 / 1000 - 1) x 100

= (331 / 1000) x 100

= 33.1%

L.H.S. = R.H.S

Hence Proved

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