Surface Areas and Volumes

A cylindrical vessel 32 cm high and 18 cm as the radius of the base is filled with sand. This is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, the radius of its base is

A solid metallic cylinder of base radius 3 cm and height 5 cm is melted to form cones, each of height 1 cm and base radius 1 mm. The number of cones is

A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is

A cube whose edge is 20 cm long, has circles on each of its faces painted black. What is the total area of the unpainted surface of the cube if the circles are of the largest possible areas ?

Three cubes each of volume 216 m3 are joined end to end. The surface area of the resulting solid is

A cube of side 4 cm is cut into a number of cubes, each of side 2 cm. The number of cubes will be