List of top Engineering Mathematics Questions on Geometry

The distance between the two points of intersection of \(x^{2}+y=7\) and \(x+y=7\) (rounded off to two decimal places) is __________________.
Which one of the following shapes can be used to tile (completely cover by repeating) a flat plane, extending to infinity in all directions, without leaving any empty spaces in between them? The copies of the shape used to tile are identical and are not allowed to overlap.
In the given figure, PQRS is a parallelogram with \(PS=7\) cm, \(PT=4\) cm and \(PV=5\) cm. What is the length of \(RS\) in cm? (The diagram is representative.)
A line of symmetry is defined as a line that divides a figure into two parts in a way such that each part is a mirror image of the other part about that line. The given figure consists of 16 unit squares arranged as shown. In addition to the three black squares, what is the minimum number of squares that must be coloured black, such that both \(PQ\) (vertical) and \(MN\) (the bottom-left to top-right diagonal) form lines of symmetry? (The figure is representative)
Let \( \Gamma \) be the positively oriented circle \( x^2 + y^2 = 9 \) in the xy-plane. If \[ \oint_{\Gamma} (3y + e^x \sin x) \, dx + \left( 7x + \sqrt{e^y + 2} \right) \, dy = \alpha \pi, \] where \( \alpha \) is a real constant, then \( \alpha \) is equal to ________.
The height of a right circular cone of maximum volume that can be enclosed within a hollow sphere of radius \(R\) is