Question

the circles are identical. find the circumference of each circle. express your answer in terms of $x$ or rounded to the nearest tenth place. $c = pi d$

Explanation:

Step1: Equate radius and diameter relationship

Since the circles are identical, the diameter of the first circle is equal to the diameter of the second circle. The diameter of a circle is twice the radius. So, \(2\times6x=10x + 4\).
$$12x=10x + 4$$

Step2: Solve for \(x\)

Subtract \(10x\) from both sides of the equation.
$$12x-10x=10x + 4-10x$$
$$2x=4$$
Divide both sides by 2.
$$x = 2$$

Step3: Find the diameter

Substitute \(x = 2\) into the expression for the diameter of the second - circle (we could also use the first - circle's diameter expression). The diameter \(d=10x + 4\), so \(d=10\times2+4=24\).

Step4: Calculate the circumference

Use the formula \(C=\pi d\). Substitute \(d = 24\) into the formula.
$$C = 24\pi\approx24\times3.14 = 75.4$$

Answer:

\(75.4\)