Proportions in Measurement

How do you find the area of a sector of a circle?

A sector is a portion of a circle. The area of a sector can be found by setting up a proportion using the angle measure of the sector, the central angle of the circle, and the area of the entire circle.

Let’s try an example. Find the area of a sector with an angle of 20˚ in a circle with radius 15 meters.

The entire area of the circle would be  square meters.

The area of the sector is proportionate to the ratio of the angle of the sector over the central angle of the circle.

Thus, the area of the sector would equal  square meters.

How do you find arc lengths?

Finding an arc length is similar to finding the area of a sector. The arc length is a part of the circumference of a circle, so its length is proportionate in a way similar to the way a sector’s area is proportionate to its angle.

Find the arc length of the sector of the circle described in the previous example.

The circle has a circumference of .

The arc length can be found using a proportion.

How do proportions apply to scale drawings?

Maps of states or drawings of buildings are not drawn life sized because it would never fit on the paper. Instead a scale drawing is made. The scale is usually identified on the map or drawing.

Let’s try an example. Find the length of the actual car if a  scale model is 12 inches long.

The ratio of the length of the model to the actual car is .