To determine the volume of a cone, we can use the formula:

In this equation, $V$ represents the volume of the cone, $r$ is the radius of the base, and $h$ is the height of the cone.

For this particular problem, we are provided with the diameter of the cone’s base, which measures 10 cm. To find the radius, we divide the diameter by 2. Thus, the radius $r$ can be calculated as follows:

Additionally, the height $h$ of the cone is given as 7 cm.

Now, we can substitute these values into the volume formula:

To solve this, we first calculate the radius squared:

Next, we multiply this result by the height:

Then, we multiply by $\pi$:

Finally, we divide this product by 3 to find the volume:

Using the approximate value of $\pi \approx 3.14$, we can estimate the volume as follows:

Calculating the numerator:

Now, we divide this by 3:

Therefore, the volume of the cone is approximately $183.17$ cubic centimeters.