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GMAT Math : Geometry

Example Questions

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Example Question #1 : Geometry

How many degrees does the hour hand on a clock move between 3 PM and 7:30 PM?

Explanation:

An hour hand rotates 360 degrees for every 12 hours, so the hour hand moves .

There are 4.5 hours between 3 PM and 7:30 PM, so the total degree measure is

.

Example Question #2 : Geometry

If a sector covers  of a circle, what is the angle of the sector?

Explanation:

One full rotation of a circle is , so if a sector covers  of a circle, its angle will be  of . This gives us:

Example Question #3 : Geometry

A given sector covers  of a circle. What is the corresponding angle of the sector?

Explanation:

A circle comprises , so a sector comprising  of the circle will have an angle that is  of .

Therefore:

Example Question #4 : Geometry

A given sector of a circle comprises  of the circle. What is the corresponding angle of the sector?

Explanation:

A circle comprises , so a sector comprising  of the circle will have an angle that is  of .

Therefore:

Example Question #5 : Geometry

The hour hand on a clock moves from 3PM to 6PM. How many degrees does the hour hand move?

Explanation:

The hour hand moves around a circle from 3PM to 6PM. Since there are 12 hours on a clock and the hand is moving through 3 of them, the hand is moving through a sector comprising  of the circle because,

.

Since a circle has , the angle of the sector is:

Example Question #6 : Geometry

A sector of a circle has a central angle equal to 45 degrees. What percentage of the circle is comprised by the sector?

Explanation:

The entire circle is 360 degrees, therefore we can set up proportions and cross multiply.

Example Question #7 : Geometry

Consider the Circle :

(Figure not drawn to scale.)

Suppose sector  covers an area of . What percentage of the area of the circle does sector  cover?

Explanation:

To find the percentage of the area of the circle that sector  covers, divide the area of sector  by the total area of the circle:

Area of the circle:

Percentage:

To go from a decimal to a percent, multiply by . This gets us to , the correct answer.

Example Question #8 : Geometry

Circle T represents a round birthday cake. If the first slice will have a central angle of  degrees, what percentage of the total cake is in the first slice?

Explanation:

In this question, the slice of cake can be thought of as a sector. We are given that its central angle is 80 degrees and asked to find what percentage of the whole it represents. Straightforward division is all we need here. We are not give a radius or any way of finding one. All we need to find is the percentage of the whole. To do that, recall that a circle has 360 degrees total and compute the following:

From here multiply by 100 to get the percentage.

So the first slice represents about 22.2% of the total cake!

Example Question #9 : Geometry

If a sector has an angle of , what percentage of the circle's area is covered by the sector?

Explanation:

The percentage of a circle covered by a sector is equal to the angle of the sector divided by the full measure of the circle, . The given sector has an angle of , so whatever percent this is of  will tell us what percent of the circle's area is covered by the sector:

Example Question #10 : Geometry

What percentage of a circle is a sector if the angle of the sector is ?