Volume of a Right Cylinder: Finding the Height

What is the height of a can of soda modeled as a right cylinder?

Santiago measures the radius of the can as 2.1 cm and its volume as 129 cubic centimeters. What is the height of the can in centimeters?

Answer:

The height of the can is approximately 5.0 cm when the volume and radius are given.

A right circular cylinder can be visualized as a three-dimensional shape with parts perpendicular to their base and closed circular surface. It has two parallel bases on both ends, creating a cylindrical body. When a can of soda is modeled as a right cylinder, its dimensions are essential in determining its height.

The formula to calculate the volume of a cylinder is [tex]V = \pi r^2 h[/tex], where V is the volume, r is the radius, and h is the height of the cylinder.

In the case of Santiago's measurement, the volume of the can is given as 129 cubic centimeters, and the radius is measured at 2.1 cm. By substituting these values into the formula, we can solve for the height:

[tex]129 = \pi (2.1)^2 h[/tex]

Simplifying the equation:

[tex]h = 129 / (\pi (2.1)^2)[/tex]

Therefore, the height of the can is approximately 5.0 cm when rounded to the nearest tenth.

Understanding how to calculate the volume of a right cylinder is essential in various real-life scenarios, such as determining the capacity of containers or objects modeled as cylinders.