Circles, sectors and arcs

Last updated: 16 Nov 2008

First some 'circle' vocabulary.

Circumference

The edge of a circle.

Diameter

A line which joins two points on the circumference of the circle passing through the center of the circle.

Radius

A line which joins the center of the circle to the circumference.

Chord

A line which joins two points on the circumference of the circle.

Tangent

A line which touches the circumference at only one point. A tangent is always perpendicular to a radius or diameter which touches the circumference in the same place.

Area

The area of a circle is PI times the radius squared.

You will not usually need to know the value of PI but just in case it does come up a test you should be aware that it is a little bit more than 3. A good decimal approximation is 3.1 or 3.14 and the fraction 22/7 also gives a good approximation.

Circumference

The length of the circumference of a circle is 2 times PI times the radius.

GMAT students commonly mix up these formulas, if you find you are using the wrong formula try to remember that area comes in square units (meters squared, m², or centimeters squared, cm²) and so it is the area formula which has radius squared in it.

Sectors and arcs

A sector is like a slice of pizza, it is just a part of circle cut out by two radii. An arc is part of the circumference of the circle.

Length of an arc

If you are asked to calculate the length of an arc you should work out the length of the whole circumference and then take the appropriate fraction of that, remembering that there are 360° in a complete circle.

For example. If we were to work out the length of an arc with radius 5 and an angle of 60° then we would first work out the circumference of the entire circle and then multiply by the fraction of the circle that the sector covers (60° out of 360°).

Area of a sector

Similarly if you are asked to calculate the area of a sector you should work out the area of the whole circle and then take the appropriate fraction of that, remembering that there are 360° in a complete circle.

For example. If we were to work out the area of the sector with radius 6 and an angle of 120° which is shown in the diagram above then we would first work out the area of the entire circle and then multiply by the fraction of the circle that the sector covers (120° out of 360°).

Next page: Cuboids and cylinders