A cylinder has a lateral area of $120\pi$ square meters and a height of 7 meters. We need to find the radius of the cylinder, rounded to the nearest tenth.

1. Problem Description

A cylinder has a lateral area of $120\pi$ square meters and a height of 7 meters. We need to find the radius of the cylinder, rounded to the nearest tenth.

2. Solution Steps

The lateral area of a cylinder is given by the formula:

$LA = 2\pi rh$, where $r$ is the radius and $h$ is the height.

We are given that $LA = 120\pi$ and $h = 7$. We can substitute these values into the formula and solve for $r$.

$120\pi = 2\pi r(7)$

Divide both sides by $\pi$:

$120 = 2r(7)$

$120 = 14r$

Divide both sides by 14:

$r = \frac{120}{14} = \frac{60}{7}$

Now, we approximate the value of $r$:

$r \approx 8.5714$

Rounding to the nearest tenth, we get $r \approx 8.6$.

3. Final Answer

8.6