Question

Given a sphere of diameter, d. What is the percentage increase in its volume when surface area increases by 21%?

Answer 1

S1 = Pi * D1^2
solve for D1
 D1 = sqrt( S1 / pi ) S2 = Pi * D2^2
 S2 = 1.21*S1
S2= 1.21 * Pi * D1^2
 1.21 * Pi * D1^2=
Pi * D2^2
 D2 D2 = sqrt( 1.21 * D1^2)
  Now V2 = pi/6 * D2^3. V2
 = pi/6 ( sqrt(1.21*D1^2))^3 V2
= pi/6 * (1.21 * D1^2)^(3/2) V2
= pi/6 * 1.21^(3/2) * D1 ^3 = (pi/6 * D1^3) * 1.21^3/2 = V1 * 1.21 ^(3/2)
=43% approximately