The kiosk consists of a cylinder and a cone. We need to find the total volume of the kiosk which is the sum of the volume of the cylinder and the volume of the cone. The cylinder has a diameter of 5 meters and a height of 3 meters. The cone has a height of 2 meters, and the diameter of the base of the cone is the same as that of the cylinder, which is 5 meters.

1. Problem Description

The kiosk consists of a cylinder and a cone. We need to find the total volume of the kiosk which is the sum of the volume of the cylinder and the volume of the cone. The cylinder has a diameter of 5 meters and a height of 3 meters. The cone has a height of 2 meters, and the diameter of the base of the cone is the same as that of the cylinder, which is 5 meters.

2. Solution Steps

First, we calculate the volume of the cylinder. The formula for the volume of a cylinder is:

$V_{cylinder} = \pi r^2 h$

where $r$ is the radius and $h$ is the height.

The diameter is 5 meters, so the radius is $r = \frac{5}{2} = 2.5$ meters.

The height is $h = 3$ meters.

$V_{cylinder} = \pi (2.5)^2 (3) = \pi (6.25)(3) = 18.75\pi$

Next, we calculate the volume of the cone. The formula for the volume of a cone is:

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

where $r$ is the radius and $h$ is the height.

The diameter is 5 meters, so the radius is $r = \frac{5}{2} = 2.5$ meters.

The height is $h = 2$ meters.

$V_{cone} = \frac{1}{3} \pi (2.5)^2 (2) = \frac{1}{3} \pi (6.25)(2) = \frac{12.5}{3} \pi \approx 4.1667\pi$

Now, we find the total volume by adding the volume of the cylinder and the volume of the cone:

$V_{total} = V_{cylinder} + V_{cone} = 18.75\pi + \frac{12.5}{3}\pi = (18.75 + \frac{12.5}{3})\pi = (18.75 + 4.1667)\pi = 22.9167\pi$

$V_{total} \approx 22.9167 * 3.14159 \approx 72.002$

Rounding to the nearest cubic meter, we get 72 cubic meters.

3. Final Answer

72