We need to find the approximate volume of a cylinder. The diameter of the cylinder is 12 cm, and its height is 13 cm. We need to round the answer to the nearest tenth.

1. Problem Description

We need to find the approximate volume of a cylinder. The diameter of the cylinder is 12 cm, and its height is 13 cm. We need to round the answer to the nearest tenth.

2. Solution Steps

First, find the radius of the cylinder. The radius $r$ is half of the diameter $d$, so $r = d/2$.

$r = 12 \text{ cm} / 2 = 6 \text{ cm}$

Next, find the area of the base of the cylinder. The base is a circle, so the area $A$ is given by $A = \pi r^2$.

$A = \pi (6 \text{ cm})^2 = 36\pi \text{ cm}^2$

Then, find the volume of the cylinder. The volume $V$ is given by $V = A \times h$, where $h$ is the height of the cylinder.

$V = 36\pi \text{ cm}^2 \times 13 \text{ cm} = 468\pi \text{ cm}^3$

Using a calculator to approximate $\pi$, we get:

$V \approx 468 \times 3.14159 \text{ cm}^3 \approx 1470.265 \text{ cm}^3$

Rounding to the nearest tenth, we have $V \approx 1470.3 \text{ cm}^3$.

3. Final Answer

1470.3