The area of a circle is given as $132.7$ square centimeters. We need to find the diameter of the circle, rounded to the nearest tenth.

1. Problem Description

The area of a circle is given as $132.7$ square centimeters. We need to find the diameter of the circle, rounded to the nearest tenth.

2. Solution Steps

We know the formula for the area of a circle is:

$A = \pi r^2$, where $A$ is the area and $r$ is the radius.

We are given $A = 132.7$. We can use this to find the radius.

$132.7 = \pi r^2$

$r^2 = \frac{132.7}{\pi}$

$r = \sqrt{\frac{132.7}{\pi}}$

Using $\pi \approx 3.14159$,

$r = \sqrt{\frac{132.7}{3.14159}} = \sqrt{42.240} \approx 6.50$

Now we know that the diameter $d$ is twice the radius, so

$d = 2r$

$d = 2(6.50) = 13.0$

Calculating again with higher precision:

$r^2 = \frac{132.7}{\pi} \approx 42.2400487$

$r = \sqrt{42.2400487} \approx 6.49923442$

$d = 2r \approx 2 \cdot 6.49923442 \approx 12.99846884 \approx 13.0$

3. Final Answer

13.0 cm