Circles - Geometry - General Aptitude (GA) Previous Year Questions

It is quarter past three in your watch. The angle between the hour hand and the minute hand is ________.

A circle with centre O is shown in the figure. A rectangle PQRS of maximum possible area is inscribed in the circle. If the radius of the circle is \(a\), then the area of the shaded portion is ________.

Four identical cylindrical chalk-sticks, each of radius \( r = 0.5 \) cm and length \( l = 10 \) cm, are bound tightly together using a duct tape as shown in the following figure.
The width of the duct tape is equal to the length of the chalk-stick. The area (in cm\(^2\)) of the duct tape required to wrap the bundle of chalk-sticks once, is

The city of Atlantis was crafted by the God of the seas, Poseidon. It was made of alternating concentric circular rings of land (shaded) and water (not shaded) as represented in the figure (not to scale). The radius of Inner Island was 2.5 stades (a unit of length used in ancient Greece). The water surrounding Inner Island was one stade wide (length AB). This was surrounded by two pairs of alternating rings of land and water. The first pair of land and water was two stades wide each (lengths BC and CD), and the outer pair is three stades wide each (lengths DE and EF).
The ratio of the surface area of the land to that of the water in the city of Atlantis is ______ (round off to two decimal places).