All GMAT Math Resources
Example Questions
Example Question #61 : Geometry
The arc
of a circle measures . The chord of the arc, , has length . Give the radius of the circle.
A circle can be divided into four congruent arcs that measure
.
If the four (congruent) chords of the arcs are constructed, they will form a square with sides of length
. The diagonal of a square has length times that of a side, which will be
A diagonal of the square is also a diameter of the circle; the circle will have radius half this length, or
Example Question #301 : Problem Solving Questions
Two circles in the same plane have the same center. The larger circle has radius 10; the area of the region between the circles is
. What is the radius of the smaller circle?
The area of a circle with radius
is .Let
be the radius of the smaller circle. Its area is . The area of the larger circle is . Since the area of the region between the circles is , and is the difference of these areas, we have
The smaller circle has radius
.Example Question #13 : Calculating The Length Of A Radius
A
arc of a circle measures . Give the radius of this circle.
A arc of a circle is
of the circle. Since the length of this arc is
, the circumference is
this, or
The radius of a circle is its circumference divided by
; therefore, the radius is
Example Question #14 : Calculating The Length Of A Radius
The arc
of a circle measures . The chord of the arc, , has length . Give the length of the radius of the circle.
A circle can be divided into
congruent arcs that measure.
If the
(congruent) chords are constructed, the figure will be a regular hexagon. The radius of this hexagon will be equal to the length of one side - one chord of the circle; this radius will coincide with the radius of the circle. Therefore, the radius of the circle is the length of chord , or .Example Question #15 : Calculating The Length Of A Radius
If a monster truck's wheels have circumference of
, what is the distance from the ground to the center of the wheel?
If a monster truck's wheels have circumference of
, what is the distance from the ground to the center of the wheel?
This question is asking us to find the radius of a circle. the distance from the outside of the circle to the center is the radius. We are given the circumference, so use the following formula:
Then, plug in what we know and solve for r
Example Question #311 : Gmat Quantitative Reasoning
Two circles in the same plane have the same center. The smaller circle has radius 10; the area of the region between the circles is
. What is the radius of the larger circle?
The area of a circle with radius
is .Let
be the radius of the larger circle. Its area is . The area of the smaller circle is . Since the area of the region between the circles is , and is the difference of these areas, we have
The smaller circle has radius
.All GMAT Math Resources
