June 1997, Paper 4 A child's toy consists of a cone inside a sphere. The radius
of the sphere, OA, is 6 cm and the radius of the base of the
cone, AC, is 3.6 cm.
(The volume of a sphere of radius R is TR%. The volume
of a cone of base radius r and height h is žarh.)
a Show that VOC, the height of the cone, is 10.8 cm.
b Calculate
i the volume of the sphere
ii the volume of the cone
iii the percentage of the volume of the
sphere not occupied by the cone.
o
6 cm
ac
A
B
3.6 cm
12.