Question 1122921
Write a formula that expresses the radius of a circle in cm, r, in terms of the circumference of the circle in inches, C. 


the formula for circumference of a circle is C = 2 * pi * r
C is the circumference, r is the radius.


if you solve this equation for r, you will get:
r = C / (2 * pi).


Write a formula that expresses the area of the circle in cm2, A, in terms of the radius of the circle in cm, r. 


the formula for the area of a circle is A = pi * r^2.
A is the area and r is the radius.


Write a formula that expresses the area of the circle in cm2, A, in terms of the circumference of the circle in inches, C. 


the formula for the circumference of a circle C = 2 * pi * r


the formula for the area of a circle is A = pi * r^2.


in the formula of C = 2 * pi * r, solve for r to get r = C / (2 * pi)


in the formula of A = pi * r^2, replace r with C / (2 * pi) to get:


A = pi * (C / (2 * pi)) ^ 2


Suppose the function f determines the area of the circle in cm2 given the circumference of the circle in inches, C. Write a function formula for f. 


the function f determines the area of the circle in square centimeters, given the circumference of the circle in inches.


the formula for the circumference of the circle is C = 2 * pi * r.


solve this formula for r to get r = C / (2 * pi)


the formula for the area of the circle is A = pi * r^2.


replace r in this formula with C / (2 * pi) to get:


A = pi * (C / (2 * pi)) ^ 2.


now C is in inches and you want A in square centimeters.


the conversion factor from inches to centimeters is:


1 inch = 2.54 centimeters


therefore, if the circumference is in inches, you would multiply it by 2.54 to get the equivalent value in centimeters.


you formula for A in terms of C would become:


A = pi * (C / (2 * pi) * 2.54) ^ 2.


this could also be written as:


A = pi * (C / (2 * pi)) ^ 2 * 2.54 ^ 2.