if c + 12r what is the area of a circle step by step
To find the area of a circle, you need to know the radius (r) of the circle. Since the equation c + 12r is given, we can assume that c represents the circumference of the circle and r represents the radius.
Step 1: Write the formula for the circumference of a circle
The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle.
Step 2: Substitute the given equation c + 12r
c + 12r = 2πr
Step 3: Solve for the circumference
c = 2πr - 12r
c = r(2π - 12)
Step 4: Substitute the formula for circumference into the area formula
The formula for the area of a circle is A = πr^2. Substitute the formula for the circumference (2πr - 12r) into the area formula.
A = π(r^2)
A = π(r(2π - 12))^2
A = π(2π - 12)^2
Step 5: Simplify the expression
A = π(4π^2 - 48π + 144)
A = 4π^3 - 48π^2 + 144π
Therefore, the area of the circle is given by the expression 4π^3 - 48π^2 + 144π.