S=4πr2 solve for r. divide both sides by 4π.
S/4π= r2 square both sides
sqrt(S/4π)= r plug in your surface area for S
for example:
sqrt(500m2/4π) = r
r = 6.3 meters
S/4π= r2 square both sides
sqrt(S/4π)= r plug in your surface area for S
for example:
sqrt(500m2/4π) = r
r = 6.3 meters
Grab a pen and get ready to jot this down:
r = √(S/4π)
That's right! The radius of a sphere, my friend, is given by the square root of S divided by 4π. Now you have a formula that shows r's dependence on S. Keep smiling and enjoy your mathematics journey!
Given: Surface Area of a sphere, S = 4π·r^2
We want to find r in terms of S.
Steps to rearrange the formula:
1. Divide both sides of the equation by 4π: S / (4π) = (4π·r^2) / (4π)
This simplifies to: S / (4π) = r^2
2. Take the square root of both sides of the equation: √(S / (4π)) = √(r^2)
This simplifies to: √(S / (4π)) = r
Therefore, the formula showing r's dependence on S is:
r = √(S / (4π))