Question

a sphere of volume 171500π/3cm³ is cut by a plane which is 21 cm far from centre of sphere. then what is percentage increment in the TSA of that sphere​

Answer 1

Answer:

Given, volume of the sphere = 171500π3=4πR33

171500π=4πR3

171500=4R3

R3=42875,R=35cm

In triangle OAB, OB=21 cm (given), applying Pythagorean Theorem,

R2=r2+OB2,

352=r2+212

r2=352−212=784

r=28cm

Total surface area of new sphere =4πR2+πr2+πr2=4πR2+2πr2

Percentage increment in total surface area =4πR2+2πr2−4πR24πR2∗100

=2πr24πR2∗100=r22R2∗100

=12282352∗100

=127841225∗100

=0.32∗100=32 %