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.
r=
Write a formula that expresses the area of the circle in cm2, A, in terms of the radius of the circle in cm, r.
A=
Write a formula that expresses the area of the circle in cm2, A, in terms of the circumference of the circle in inches, C.
A=
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.
f(C)=
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
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