In the figure given below, ABCD is the rectangle. AB = 14 cm, BC = 7 cm. From the rectangle, a quarter circle BFEC and a semicircle DGE are removed. Calculate the area of the remaining piece of the rectangle. (Take `pi = 22/7`).
In the given figure, ABCD is the square of side 21 cm. AC and BD are two diagonals of the square. Two semicircles are drawn with AD and BC as diameters. Find the area of the shaded region. (Take `pi = 22/7`)
Find the area of the biggest circle that can be cut from a rectangular piece of 44cm by 28 cm. Also, find the area of the paper left after cutting out the circle.
A circular hall, surmounted by a hemispherical roof, contains 5236 m3 of air. If the internal diameter of the room is equal to the height of the highest point of the roof from the floor, find the height of the hall.
A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. Find the height of the cone.