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# Working With Circles and Circular Figures Study Guide (page 2)

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Updated on Oct 5, 2011

## Surface Area of a Cylinder

When you are looking for the surface area of a cylinder, you need to find the area of two circles (the bases) and the area of the curved surface that makes up the side of the cylinder. The area of the curved surface is hard to visualize when it is rolled up. Picture a paper towel roll. It has a circular top and bottom. When you unroll a sheet of the paper towel, it is shaped like a rectangle. The area of the curved surface is the area of a rectangle with the same height as the cylinder, and the base measurement is the same as the circumference of the circle base.

Surface area of a cylinder = area of two circles + area of rectangle

= 2πr2 + bh

= 2πr2 + 2πrh

#### Examples:

Find the surface area of each cylinder. Use 3.14 for π.

## Volume of a Cylinder

Similar to finding the volume of a prism, you can find the volume of a cylinder by finding the product of the area of the base and the height of the figure. Of course, the base of a cylinder is a circle, so you need to find the area of a circle times the height.

#### Examples:

Find the volume of each cylinder. Use 3.14 for π.

## Volume of a Cone

A cone relates to a cylinder in the same way that a pyramid relates to a prism. If you have a cone and a cylinder with the same radius and height, it would take three of the cones to fill the cylinder. In other words, the cone holds one-third the amount of the cylinder.

#### Examples:

Find the volume of the cone. Use 3.14 for π.

### Surface Area of a Sphere

A sphere is the set of all points that are the same distance from some point called the center. A sphere is most likely to be called a ball. Try to find an old baseball and take the cover off of it. When you lay out the cover of the ball, it roughly appears to be four circles. Recall that the formula for finding the area of a circle is A = πr2.

#### Examples:

Find the surface area of the sphere. Use 3.14 for π.

## Volume of a Sphere

If you were filling balloons with helium, it would be important for you to know the volume of a sphere. To find the volume of a sphere, picture the sphere filled with numerous pyramids. The height of each pyramid represents the radius (r) of the sphere. The sum of the areas of all the bases represents the surface area of the sphere.

#### Examples:

Find the volume of the sphere. Use 3.14 for π.

Practice problems for these concepts can be found at: Working With Circles and Circular Figures Practice Questions.

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