Let r and h be the radius and height of the cone-I and let r and h be the radius and height of the cone-II. Given that, h h and Volume of the cone I Volume of the cone II = r h r h ⇒ r h h ´ = ⇒ r Therefore, ratio of their radii = : Progress Check . Volume of a cone is the product of its base area and . .
If the radius of the cone is doubled, the new volume will be times the original volume. . Consider the cones given in Fig. .
(i) Without doing any calculation, find out whose volume is greater? (ii) Verify whether the cone with greater volume has greater surface area. (iii) Volume of cone A : Volume of cone B = ? .
. Volume of sphere Let r be the radius of a sphere then its volume is given by V = cu. units. Demonstration cone A cone B Fig.
. cm cm cm cm Fig. . z Consider a sphere and two right circular cones of same base radius and height such that twice the radius of the sphere is equal to the height of the cones.
z Then we can observe that the contents of two cones will exactly occupy the sphere. Mensuration From the Fig. . , we see that Volume of a sphere = × (Volume of a cone) where the diameters of sphere and cone are equal to the height of the cone.
p r h p r r , ( h = ) Volume of a sphere = p r cu. units . . Volume of a hollow sphere / spherical shell (volume of the material used) Let r and R be the inner and outer radius of the hollow sphere.
Volume enclosed between the outer and inner spheres R Volume of a hollow sphere = p ( R