A field is in the form of an equilateral triangle of side 100 m. A horse is tied to a vertex of the field, with a 15 m long rope. Over what area can the horse graze? 

A shuttlecock used of playing badminton has the shape of a frustum of a cone mounted on a semi sphere. The external diameters of the frustum are 5 cm and 2 cm, the height of the entire shuttlecock is 7 cm. The external surface is of the shuttlecock is:

A cylindrical container is filled with ice cream. Its diameter is 12 cm. and height is 15 cm. The whole ice cream is distributed among 10 children in equal cones having hemispherical tops. If the height of the conical portion is twice the diameter of its base, the diameter of the ice - cream cone is – 

A corner of a cube of side length 8 m. When cut by a plane which bisects the sides of the cube, we get a pyramid whose volume is : 

A conical vessel of radius 6 cm and height 8 cm. is completely filled with water. A sphere is lowered into the water and its size is such that when it touches the sides, it is just immersed. The fraction of water that overflows is? 

A wire of length 60 m is used to enclose a field which is in the shape of a right - angled triangle. The area of the field is 150 m² then, the largest side of the field has a length of: 

The ratio between the length and breadth of a rectangular park is 3: 2. If a man cycling along the boundary of the park at the speed of 12 Km./hr. completes one round in 8 min, then the area of the park in sq.m is – 

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 ?