Solve [tex]C=2 \pi r[/tex] for [tex]r[/tex].
A. [tex]r=\frac{C \pi}{2}[/tex]
B. [tex]r=\frac{C}{2 \pi}[/tex]
C. [tex]r=2 \pi r[/tex]
D. [tex]r=\frac{2 C}{\pi}[/tex]
Answer (2)
Start with the formula for the circumference of a circle: C = 2 π r .
Divide both sides of the equation by 2 π to isolate r .
Simplify the equation to find r = 2 π C .
The solution for r is 2 π C .
Explanation
Understanding the Problem We are given the formula for the circumference of a circle, C = 2 π r , and we want to solve for r , which represents the radius of the circle. This means we want to isolate r on one side of the equation.
Isolating r To isolate r , we need to divide both sides of the equation by 2 π . This will undo the multiplication of r by 2 π .
Solving for r Dividing both sides of the equation C = 2 π r by 2 π , we get: 2 π C = 2 π 2 π r Simplifying the right side, we have: 2 π C = r Thus, r = 2 π C .
Final Answer Therefore, the solution for r is 2 π C .
Examples
Imagine you're designing a circular garden and you know the length of fencing you have available (the circumference). By solving the circumference formula for the radius, you can determine how wide to make your garden. For example, if you have 50 feet of fencing, the radius of your garden should be approximately 2 π 50 ≈ 7.96 feet. This ensures you use all your fencing and maximize the area of your garden.
To solve for r in the equation C = 2 π r , we divide both sides by 2 π to obtain r = 2 π C . Thus, the correct answer is option B .
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