A sphere of maximum volume is cut out from a solid hemisphere of radius r. The ratio of the volume of the hemisphere to that of the cut out sphere is

The capacity of a tank of dimensions (8 m x 6 m x 2.5 m) is

XYZ is an equilateral triangle with vertices X (6, -2), Y (2, - 1) and Z (4, -2). If ZA is one of its medians find the length of the median

If the perimeter of a rectangle and a square, each is equal to 80 cm and the difference of their areas is 100sq.cm. The sides of the rectangle are

The dimensions of a room are 10 m × 7m ×5 m. There are 2 doors and 3 windows in the room. The dimensions of the doors are 1 m × 3m, one window is of size 2 m× 1.5 m and the other two windows are of size 1 m × 1.5 m. The cost of painting the walls at Rs. 3 per m² is

The radii of two cones are in the ratio 2:1, their volumes are equal. Find the ratio of their heights

If the side of a square is increased by 3 cm., the area increases by 33 cm. The side of the square is

The surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 12 cm. The radius of the square is

An iron cube of side 10 cm is hammered into a rectangular sheet of thickness 0.5 cm. If the sides of the sheet are in the ratio 1 : 5, the sides are:

The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq.cm. What is the length of the rectangle?