Sphere, Hemisphere and Spherical Shell
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Let's commence questions....
1. Find the volume and surface area of a sphere of radius 4.2 cm?
(Take pi = 22/7)
2. Find the volume and the total surface area of a hemisphere of radius 3.5 cm?
(Use pi= 22/7)
3. The internal and external diameters of a hollow hemispherical vessel are 24 cm and 25 cm respectively. The cost to paint 1 cm square the surface is Re 0.05. Find the total cost to paint the vessel all over?
(Use pi = 22/7)
4. A hollow spherical shell is made of a metal of density 4.9 g/cm3. If its internal and external
radii are 10 cm and 12 cm respectively, find the weight of the shell?
5. A sphere and a cube have the same surface. Show that the ratio of the volume of sphere to
that of the cube is √6 : .
6. A measuring jar of internal diameter 10 cm is partially filled with water. Four equal spherical balls of diameter 2 cm each are dropped in it and they sink down in the water completely. What will be the change in the level of water
in the jar?
7. Metal spheres, each of radius 2 cm are packed into a rectangular box of internal dimension 16 cm × 8 cm × 8 cm. When 16 spheres are packed the box is filled with preservative liquid. Find the volume of this liquid. Give your answer to the nearest integer?
(use π=669 ∕213)
8. A vessel is in the form of an inverted cone. Its height is 8 cm and the radius is 5 cm. It is filled with water upto the brim. When lead shots each of which is a sphere of radius 0.5 cm are dropped into the vessel, one fourth of the water flows out. Find the number of lead shots dropped into the vessel?
9. A solid is composed of a cylinder with hemispherical ends. If the whole length of
the solid is 108 cm and the diameter of the hemispherical ends is 36 cm, find the cost of
polishing the surface of the solid at the rate of 7 paisa per sq cm?
(Use pi = 22/7)
10. Three identical balls fit snugly into a cylindrical can. The radius of the spheres
equal the radius of the can, and the balls just touch the bottom and the top of the can. If
the formula for the volume of a sphere is V= (4/3)πr³
, what fraction of the volume of the can is taken up by the balls?
11. A sphere of maximum volume is cut out from a solid hemisphere of radius r. Find the ratio
of the volume of the hemisphere to that of the sphere?
12. The ratio of the volumes of a right circular cylinder and sphere is 3 : 2. If the radius of the sphere is double the radius of the base of the cylinder, find the ratio of the surface areas of the cylinder and sphere. Find the volume and surface area of a cylinder and sphere?
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