verified that cylinder B with greater volume has a greater surface area. (iii) Volume of cylinder Volume of cylinder B = . = Therefore, ratio of the volumes of cylinders A and B is : . Fig.
. 21cm cm cylinder A 21cm cm cylinder B Mensuration . . Volume of a right circular cone Let r and h be the radius and height of a cone then its volume V r h = cu.
units. Demonstration From, Fig. . we see that, × (Volume of a cone) = Volume of cylinder = p r h cu.
units Volume of a cone = p r h cu. units Example . The volume of a solid right circular cone is 11088 cm . If its height is cm then find the radius of the cone.
Solution Let r and h be the radius and height of the cone respectively. Given that, volume of the cone = 11088 cm p r h = 11088 ´ ´ ´ = 11088 r = Therefore, radius of the cone r = cm Thinking Corner . Is it possible to find a right circular cone with equal (a) height and slant height (b) radius and slant height (c) height and radius. .
There are two cones with equal volumes. What will be the ratio of their radius and height? Fig. .
C C C C C C z Consider a right circular cylinder and three right circular cones of same base radius and height as that of the cylinder. z The contents of three cones will exactly occupy the cylinder. Example . The ratio of the volumes of two cones is : .
Find the ratio of their radii if the height of second cone is double the height of the first. Solution