Question

the circle has a circumference of 81.64. using 3.14 to approximate $pi$, find the value of x.

Explanation:

Step1: Recall circumference formula

The formula for the circumference of a circle is $C = 2\pi r$. Here $C = 81.64$ and $\pi\approx3.14$, and the radius $r=x + 9$.

Step2: Substitute values into formula

Substitute into $C = 2\pi r$: $81.64=2\times3.14\times(x + 9)$.

Step3: Simplify the right - hand side

First, calculate $2\times3.14 = 6.28$. So the equation becomes $81.64=6.28\times(x + 9)$.

Step4: Distribute 6.28

$81.64=6.28x+6.28\times9$. Since $6.28\times9 = 56.52$, the equation is $81.64=6.28x + 56.52$.

Step5: Isolate the term with x

Subtract 56.52 from both sides: $81.64−56.52=6.28x$. So $25.12 = 6.28x$.

Step6: Solve for x

Divide both sides by 6.28: $x=\frac{25.12}{6.28}=4$.

Answer:

$4$