The area of a circle can be calculated by the formula S=π ·r^2, where r is the
radius of the circle, or by the formula S=π ·d/4, where d is the diameter of
the circle. Write a formula expressing:
r in terms S
and d in terms of S
To express r in terms of S, we need to rearrange the formula S = π · r^2.
Step 1: Divide both sides of the equation by π to isolate r^2.
S/π = r^2
Step 2: Take the square root of both sides to solve for r.
√(S/π) = r
Therefore, the formula expressing r in terms of S is:
r = √(S/π)
To express d in terms of S, we can use the formula S = π · d/4 and rearrange it.
Step 1: Multiply both sides of the equation by 4/π to get rid of the fraction.
(4/π)S = d
Therefore, the formula expressing d in terms of S is:
d = (4/π)S
To express the radius (r) in terms of the area (S), we can rearrange the formula S = π · r^2. The formula for the radius in terms of the area is:
r = √(S/π)
So, if you know the area of the circle (S), you can use this formula to calculate the radius (r).
To express the diameter (d) in terms of the area (S), we can rearrange the formula S = π · d/4. The formula for the diameter in terms of the area is:
d = √(4S/π)
So, if you know the area of the circle (S), you can use this formula to calculate the diameter (d).
r = √(S / π)
d = √(4 S / π) = 2 √(S / π)