Volume of a Cylinder
The volume of a cylinder is the product of the area of its base and its height. Because a cylinder has a circular base, the volume of a cylinder is:
where r is the radius of the circular base and h is the height. Try to find the volume of the cylinder below:
This cylinder has a radius of 4 and a height of 6. Using the volume formula:
Surface Area of a Cylinder
The surface area of a cylinder is the sum of the areas of the two bases and the lateral face of the cylinder. The bases are congruent circles, so their areas can be found easily. The lateral face is the tubing that connects the two bases. When “unrolled,” the lateral base is simply a rectangle whose length is the circumference of the base and whose width is the height of the cylinder. Therefore, the surface area of a cylinder is given by this formula:
where r is the radius and h is the height. As with finding the volume of a cylinder, finding the surface area involves plugging the height and radius of the base into the formula. To find the surface area of the cylinder in the practice example on volume,
just plug the values into the formula:
