SOLUTION: Can someone help me with this problem please? The surface area of a sphere is directly proportional to the square of its radius. The volume of the sphere is directly proportiona

Algebra ->  Proportions -> SOLUTION: Can someone help me with this problem please? The surface area of a sphere is directly proportional to the square of its radius. The volume of the sphere is directly proportiona      Log On


   

Question 125791: Can someone help me with this problem please?
The surface area of a sphere is directly proportional to the square of its radius. The volume of the sphere is directly proportional to the cube of the radius. Find the percentage increase in volume of the sphere if the surface area is increased by 25%.
My work so far:
Surface Area = S = 4πr^2
Radius = r
Volume = V = 4/3 πr^3
S ∝ r^2
V ∝ r^3
125% = 5/4
I tired to calculate the value of V/S as a start and got V/(S )= r/3
Then I got stuck. Hope you can help
Answer by kev82(151) About Me  (Show Source):
You can put this solution on YOUR website!
The surface area is proportional to the square of the radius, so if we have increased the surface area by 25% (multipled by 1.25) then we have increased the radius by sqrt(1.25). This is because the radius increases as the square root of the surface area. Now the volume increases as the cube of the radius and the radius has increased by sqrt(1.25) so the volume has increased by (sqrt(1.25))^3 which is roughly 40%.