7.5 Conversion of Solids from one shape to another with no change in Volume · Part 3

has base radius r units and height h units, the water is poured into a cylindrical flask of base radius xr units. Find the height of water in the cylindrical flask. Fig. . Mensuration . A solid right circular cone of diameter cm and height cm is melted to form a hollow sphere. If the external diameter of the sphere is cm, find the internal diameter. . Seenu’s house has an overhead tank in the shape of a cylinder. This is filled by pumping water from a sump (underground tank) which is in the shape of a cuboid. The sump has dimensions m ´ . m ´ m. The overhead tank has its radius of cm and height cm. Find the volume of the water left in the sump after the overhead tank has been completely filled with water from the sump which has been full, initially. . The internal and external diameter of a hollow hemispherical shell are cm and cm respectively. If it is melted and recast into a solid cylinder of diameter cm, then find the height of the cylinder. . A solid sphere of radius cm is melted into a hollow cylinder of uniform thickness. If the external radius of the base of the cylinder is cm and its height is cm, then find the thickness of the cylinder. . A hemispherical bowl is filled to the brim with juice. The juice is poured into a cylindrical vessel whose radius is % more than its height. If the diameter is same for both the bowl and the cylinder then find the percentage of juice that can be transferred from the bowl into the cylindrical vessel. Exercise . Multiple choice questions . The curved surface area of a right circular cone of height cm and base diameter cm is ( A ) p cm ( B ) p cm (