cu. units . . Volume of solid hemisphere Let r be the radius of the solid hemisphere.
Volume of the solid hemisphere = (volume of sphere) p r Volume of a solid hemisphere = p r cu. units . . Volume of hollow hemisphere (volume of the material used) Let r and R be the inner and outer radius of the hollow hemisphere.
Volume of hollow hemisphere Volume of outer hemisphere Volume of inner hemisphere R Volume of a hollow hemisphere = p ( R cu. units Thinking Corner A cone, a hemisphere and a cylinder have equal bases. The heights of the cone and cylinder are equal and are same as the common radius. Are they equal in volume?
Fig. . R Example . The volume of a solid hemisphere is 29106 cm .
Another hemisphere whose volume is two-third of the above is carved out. Find the radius of the new hemisphere. Solution Let r be the radius of the hemisphere. Given that, volume of the hemisphere = 29106 cm Now, volume of new hemisphere = (Volume of original sphere) 29106 Volume of new hemisphere = 19404 cm p r = 19404 r = × × 19404 = r = = cm Therefore, r = cm Thinking Corner .
Give any two real life examples of sphere and hemisphere. . A plane along a great circle will split the sphere into parts. .
If the volume and surface area of a sphere are numerically equal, then the radius of the sphere is . Example . Calculate the mass of a hollow brass sphere if the inner diameter is cm and thickness is mm, and whose density is . g/ cm .
( Hint: mass = density × volume )