We are given a cone with radius $r = 2.6$ cm and slant height $l = 18$ cm. We need to find the volume of the cone and round the answer to the nearest tenth.

1. Problem Description

We are given a cone with radius $r = 2.6$ cm and slant height $l = 18$ cm. We need to find the volume of the cone and round the answer to the nearest tenth.

2. Solution Steps

First, we need to find the height $h$ of the cone. We can use the Pythagorean theorem since the radius, height, and slant height form a right triangle:

$r^2 + h^2 = l^2$

Plugging in the given values:

$(2.6)^2 + h^2 = (18)^2$

$6.76 + h^2 = 324$

$h^2 = 324 - 6.76$

$h^2 = 317.24$

$h = \sqrt{317.24}$

$h \approx 17.81123$ cm

Now, we can calculate the volume $V$ of the cone using the formula:

$V = \frac{1}{3}\pi r^2 h$

Plugging in the values for $r$ and $h$:

$V = \frac{1}{3}\pi (2.6)^2 (17.81123)$

$V = \frac{1}{3}\pi (6.76)(17.81123)$

$V \approx \frac{1}{3}\pi (120.4239)$

$V \approx \frac{1}{3}(378.346)$

$V \approx 126.115$

Rounding to the nearest tenth:

$V \approx 126.1$ cubic centimeters

3. Final Answer

The volume of the cone is approximately 126.1 cubic centimeters.