. Volume Having discussed about the surface areas of cylinder, cone, sphere, hemisphere and frustum, we shall now discuss about the volumes of these solids. Volume refers to the amount of space occupied by an object. The volume is measured in cubic units.
. . Volume of a solid right circular cylinder The volume of a right circular cylinder of base radius ‘ r ’ and height ‘ h ’ is given by V = (Base Area) × (Height) = p h r h cubic units. Therefore, Volume of a cylinder = p r h cu.
units. 6c m 8c m 12c m h Fig. . Mensuration .
. Volume of a hollow cylinder (volume of the material used) Let the internal and external radii of a hollow cylinder be r and R units respectively. If the height of the cylinder is h units then The volume V = volume of the outer cylinder volume of the inner cylinder V = R h r h p ( R r h Volume of a hollow cylinder = p ( R r h cu. units.
Example . Find the volume of a cylinder whose height is m and whose base area is m . Solution Let r and h be the radius and height of the cylinder respectively. Given that, height h = m, base area = m Now, volume of a cylinder = p r h cu.
units base area h = m Therefore, volume of the cylinder = m Thinking Corner . If the height is inversely proportional to the square of its radius, the volume of the cylinder is . . What happens to the volume of the cylinder with radius r and height h , when its (a) radius is halved (b) height is halved.
Example . The volume of a cylindrical water