The area of the largest triangle that can be inscribed in a semi-circle of radius r is²

Let a,b ,c be the sides of a right triangle,where c is the hypotenuse.The radius of the circle which touches the sides of the triangle is

The angles of a triangle are in the ratio 4:1:1.Then the ratio of largest side to the perimeter is

If the height of a right circular cone is increased by 200% and radius of the base is decreased by 50%,then the volume of the cone

A cylindrical vassel of radius 4m contains water.A solid sphere of radius 3m is lowered into water until it is completely immersed.Water level in the vessel will rise by

The ratio of outer and inner perimeters of a circular path is 23:22.If the path is 5m wide,diameter of the inner circle is