Important Key points
Example 7.24
A toy is in the shape of a cylinder surmounted by a
hemisphere. The height of the toy is 25 cm. Find the total surface
area of the toy if its common diameter is 12 cm.
Example 7.25
A jewel box (Fig. 7.39) is in the shape of a cuboid of
dimensions 30 cm 15 cm 10 cm surmounted by a half part of
a cylinder as shown in the figure. Find the volume of the box.
Example 7.26
Arul has to make arrangements for the accommodation of 150 persons
for his family function. For this purpose, he plans to build a tent which is in the shape of
cylinder surmounted by a cone. Each person occupies 4 sq. m of the space on ground and
40 cu. meter of air to breathe. What should be the height of the conical part of the tent if
the height of cylindrical part is 8 m?
Example 7.27
A funnel consists of a frustum of a cone attached to a cylindrical portion
12 cm long attached at the bottom. If the total height be 20 cm, diameter of the cylindrical
portion be 12 cm and the diameter of the top of the funnel be 24 cm. Find the outer
surface area of the funnel.
Example 7.28
A hemispherical section is cut out from one face of
a cubical block such that the diameter l of the hemisphere
is equal to side length of the cube. Determine the surface area of
the remaining solid.
Important Key Points
1. A vessel is in the form of a hemispherical bowl mounted by a hollow cylinder. The diameter is 14 cm and the height of the vessel is 13 cm. Find the capacity of the vessel.
2. Nathan, an engineering student was asked to make a model shaped like a cylinder with two cones attached at its two ends. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of the model that Nathan made.
3. From a solid cylinder whose height is 2.4 cm and the diameter 1.4 cm, a cone of the same height and same diameter is carved out. Find the volume of the remaining solid to the nearest .
4. A solid consisting of a right circular cone of height 12 cm and radius 6 cm standing on a hemisphere of radius 6 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of the water displaced out of the cylinder, if the radius of the cylinder is 6 cm and height is 18 cm.
5. A capsule is in the shape of a cylinder with two hemisphere stuck to each of its ends. If the length of the entire capsule is 12 mm and the diameter of the capsule is 3 mm, how much medicine it can hold?
6. As shown in figure a cubical block of side 7 cm is surmounted by a hemisphere. Find the surface area of the solid.
7. A right circular cylinder just enclose a sphere of radius r units.
Calculate
(i) the surface area of the sphere
(ii) the curved surface area of the cylinder
(iii) the ratio of the areas obtained in (i) and (ii).