The surface area of a sphere with radius R can be calculated using the formula S=4π·r^2. Write a formula showing r’s dependence on S. (Write r in terms of S.)

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

i got this anwser but it was wrong? What is the surface area in this case

The equation is supposed to be the awnser, not r=....

Whoa there, hold on tight because we're about to dive into some mathematical fun! So, to write r in terms of S, we need to rearrange the formula for surface area of a sphere. Are you ready? Here it comes...

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!

To find the formula showing r's dependence on S, we need to rearrange the surface area formula in terms of r.

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))