In the given figure, PQRS is square whose side is 8 cm. PQS and QPR are two quadrants. A circle is placed touching both the quadrants and the square as shown in the figure. What is the area ( in cm² ) of the circle ?

There is a circular garden of radius 21 metres. A path of width 3.5 metres is constructed just outside the garden. What is the area (in metres) of the path? 

What is the area ( in cm² ) of the circumcircle of a triangle whose sides are 6 cm , 8 cm and 10 cm respectively ? 

The base of right prism is a trapezium whose parallel sides are 11 cm and 15 cm and the distance between them is 9 cm. If the volume of the prism is 1731.6 cm³, then the height (in cm) of the prism will be:

The areas of the three adjacent faces of a cuboid are 32 cm², 24 cm² and 48cm². What is the volume of the cuboid?

Base of a right pyramid is a square. The length of diagonal of the base is $$ {12\sqrt{2}}$$ cm. If each lateral surface of the pyramid is an equilateral triangle, then its volume (in cu.cm) is

The curved surface area of a right circular cylinder of radius 2 cm is 264 cm². The height of the cylinder, in cm, is

The diameter of a roller is 84 cm and its length is 120 cm. It makes 500 complete revolutions to move once over to level a playground. Find the area of the playground.