List of top Quantitative Aptitude Questions on Geometry asked in GRE

\( AB \) is a diameter of the circle. Compare: 
Quantity A: The length of \( AB \) 
Quantity B: The average (arithmetic mean) of the lengths of \( AC \) and \( AD \). 

O is the center of the circle above. 

What is the perimeter, in meters, of a rectangular playground 24 meters wide that has the same area as a rectangular playground 64 meters long and 48 meters wide?
In the figure above, \( O \) and \( P \) are the centers of the two circles. If each circle has radius \( r \), what is the area of the shaded region?
In the \( xy \)-plane, line \( k \) is a line that does not pass through the origin. Which of the following statements individually provide(s) sufficient additional information to determine whether the slope of line \( k \) is negative?
The point with coordinates \((-6,-7)\) is the center of circle \( C \). The point \((-6,5)\) lies inside circle \( C \), and the point \((8,-7)\) lies outside circle \( C \). What is the radius of circle \( C \)?
In the \( xy \)-plane, the equation of line \( k \) is \( 3x - 2y = 0 \). Compare:
Quantity A: The \( x \)-intercept of line \( k \)
Quantity B: The \( y \)-intercept of line \( k \)
For what value of \( k \) will the system of equations \( 2x + 3y = 12 \) and \( 4x + ky = 24 \) have no solution?
A rectangle has a width of 6 units and a perimeter of 32 units. What is the length of the rectangle?
In a circle with a radius of 10, what is the area of a sector with a central angle of 72 degrees?
Solve for \( y \) in terms of \( x \) if \( 4x - 5y = 20 \).
If \( x + 1 = 3(x - 2) \), what is the value of \( x \)?
In a circle with a radius of 5, what is the length of an arc that subtends a central angle of 120 degrees?
A cube has a surface area of 54 square units. What is the volume of the cube?
A rectangle has a length that is twice its width. If the perimeter is 48 units, what is the area of the rectangle?
In triangle \( ABC \), if \( AB = 6 \), \( BC = 8 \), and \( AC = 10 \), what is the area of the triangle?
A right triangle has one leg of 5 cm and a hypotenuse of 13 cm. What is the length of the other leg?
What is the area of a triangle with a base of 8 cm and a height of 5 cm?
What is the circumference of a circle with a radius of 7 cm?
Find the length of the hypotenuse of a right triangle with legs of length 6 cm and 8 cm.
What is the volume of a cylinder with a radius of 3 cm and a height of 5 cm?
What is the area of a circle with a diameter of 10 cm?
\textit{(Use} \( \pi \approx 3.14{)}
Find the surface area of a cube with side length 4 cm.
A right triangle has legs of length 9 cm and 12 cm. What is the length of the hypotenuse?
What is the volume of a rectangular prism with length 5 cm, width 3 cm, and height 4 cm?