List of top General Aptitude Questions on Geometry asked in GATE CH, GATE BT

A thin wire is used to construct all the edges of a cube of 1 m side by bending, cutting, and soldering the wire. If the wire is 12 m long, what is the minimum number of cuts required to construct the wire frame to form the cube?

Three villages P, Q, and R are located in such a way that the distance PQ = 13 km, QR = 14 km, and RP = 15 km, as shown in the figure. A straight road joins Q and R. It is proposed to connect P to this road QR by constructing another road. What is the minimum possible length (in km) of this connecting road?
Note: The figure shown is representative.


 

Which one of the following sets of pieces can be assembled to form a square with a single round hole near the center? Pieces cannot overlap.

A sphere of radius \(r\) cm is packed in a box of cubical shape. What should be the minimum volume (in cm\(^3\)) of the box that can enclose the sphere?
A building has several rooms and doors as shown in the top view of the building given below. The doors are closed initially.
What is the minimum number of doors that need to be opened in order to go from the point P to the point Q?

The above frequency chart shows the frequency distribution of marks obtained by a set of students in an exam.
From the data presented above, which one of the following is CORRECT?
In the following diagram, the point R is the center of the circle. The lines PQ and ZV are tangential to the circle. The relation among the areas of the squares, PXWR, RUVZ and SPQT is
Two straight lines pass through the origin \( (x_0, y_0) = (0, 0) \). One of them passes through the point \( (x_1, y_1) = (1, 3) \) and the other passes through the point \( (x_2, y_2) = (1, 2) \). What is the area enclosed between the straight lines in the interval \( [0, 1] \) on the x-axis?
If $\theta$ is the angle, in degrees, between the longest diagonal of the cube and any one of the edges of the cube, then $\cos \theta =$

A polygon is convex if, for every pair of points inside the polygon, the line segment joining them lies completely inside or on the polygon. Which one of the following is NOT a convex polygon?