level – 1

1. The height of a hemisphere and a right circular cylinder are equal. If their volumes are equal, then the ratio of the radius of the hemisphere to the radius of the cylinder is:
(a) √2 : √3
(b) √3 : √2
(c) 2 : 3
(d) 3 : 2

2. A metallic hemisphere of radius r is melted and recast into a right circular cone having the same base radius r. If h is the height of the cone, then h is equal to:
(a) r
(b) 3r/2
(c) 2r
(d) 3r

3. A sphere is cut into two hemispheres. One hemisphere is used as a bowl. It takes 9 bowlfuls of this to fill a conical vessel of height 9 cm and radius 6 cm. The radius (in cm) of the original sphere is:
(a) 2
(b) 3
(c) 4
(d) 5

4. An ice-cream is formed by filling a conical cup completely and a hemisphere is formed on its open top. The height of the hemispherical part is 3.5 cm. The radius of the hemispherical part is equal to the height of the cone. Find the volume of the ice-cream (in cm³). (Take π = 22/7)
(a) 245
(b) 294
(c) 343
(d) 392

5. A hemisphere of metal is melted and recast into a right circular cylinder of diameter 14 cm and height 49 cm. The radius (in cm) of the hemisphere is:
(a) 14
(b) 21
(c) 28
(d) 35

6. A right circular cylinder is circumscribed about a hemisphere such that they share the same base. If the radius of the hemisphere is r, then the ratio of the volumes of the cylinder to the hemisphere is:
(a) 2 : 1
(b) 3 : 2
(c) 4 : 3
(d) 5 : 2

7. The radius of a hemispherical bowl is 7 cm. The capacity of the bowl is (Take π = 22/7):
(a) 686 cm³
(b) 718 cm³
(c) 1437 cm³
(d) 1078 cm³

8. The diameters of the internal and external surfaces of a hollow spherical shell are 8 cm and 14 cm respectively. If the shell is melted and recast into a solid cylinder of height 6 cm, then the diameter (in cm) of the cylinder is:
(a) 8
(b) 10
(c) 12
(d) 14

9. A hemispherical bowl of internal radius 7 cm is completely filled with a liquid. The liquid is transferred into cylindrical bottles, each of diameter 2 cm and height 7 cm. The number of bottles required to empty the bowl is:
(a) 98
(b) 147
(c) 196
(d) 294

10. A right circular cylinder of diameter 14 cm and height 21 cm is completely filled with ice-cream. The ice-cream is transferred into cones of height 7 cm and diameter 7 cm, each having a hemispherical top. The number of such cones that can be completely filled is:
(a) 6
(b) 9
(c) 12
(d) 18

11. A solid right circular cylinder of radius 7 cm and height 14 cm is completely melted and recast into hemispherical balls each of radius 3.5 cm.
(a) 16
(b) 24
(c) 28
(d) 32

12. A hollow hemispherical bowl is made of copper with outer radius 10 cm and inner radius 6 cm. The bowl is melted and recast into a solid right circular cone of base radius 8 cm. The height (in cm) of the cone formed is:
(a) 6
(b) 8
(c) 9
(d) 12

13. The radii of two solid metal spheres are 3 cm and 4 cm respectively. They are melted together to form a hollow sphere. If the external radius of the hollow sphere is 7 cm, then the thickness (in cm) of the hollow sphere is:
(a) 2
(b) 3
(c) 4
(d) 5

level – 2

1. The volume of a solid hemisphere is 4851 cm³. Then the total surface area (in cm²) of the hemisphere is:
(a) 1386
(b) 1452
(c) 1584
(d) 1664

2. A solid hemisphere has a radius of 14 cm. The curved surface area of the hemisphere (in sq. cm) is:
(a) 1056
(b) 1120
(c) 1232
(d) 1344

3. If the total surface area of a hemisphere is 36π sq. cm, then the radius of the base of the hemisphere is:
(a) 2 cm
(b) 3 cm
(c) 4 cm
(d) 6 cm

4. A toy is in the form of a cone mounted on a hemisphere. The radius of both the cone and hemisphere is 7 cm and the height of the cone is 24 cm. Find the total surface area of the toy. (Take π = 22/7)
(a) 924 cm²
(b) 968 cm²
(c) 1056 cm²
(d) 1144 cm²

5. A sphere and a solid hemisphere are made of the same material and have the same radius. The ratio of the total surface area of the sphere to the curved surface area of the hemisphere is:
(a) 1 : 1
(b) 2 : 1
(c) 3 : 1
(d) 4 : 1

6. A hemisphere and a right circular cone stand on equal circular bases. If the height of the cone is equal to the radius of the hemisphere, then the ratio of their curved surface areas is:
(a) 1 : 1
(b) 2 : 1
(c) 3 : 2
(d) 2 : 3

7. Two hollow spheres are made from the same metal sheet. The diameters of the spheres are 28 cm and 14 cm respectively. The ratio of the area of metal sheets required for making the two spheres is:
(a) 1 : 2
(b) 2 : 1
(c) 4 : 1
(d) 8 : 1

ANSWERS