Volume & Surface Areas

1

A sphere of maximum volume is cut out from a solid hemisphere of radius r, The ratio of the volume of the hemisphere  to that of the cut out  sphere is  :

A. 3 : 2
B. 4 : 1
C. 4 : 3
D. 7 : 4

2

A hemisphere and a cone have equal bases . If their height are also equal, then the ratio of their  curved surface will be :

A. 1 : 2
B. 2 : 1
C. 1 : `sqrt(2)`
D. `sqrt(2)` : 1

3

A hemisphere of load of radius 6 cm is cast into a right circular cone of height 76 cm . The radius of the  base of the  cone is  :

A. 1.4 cm
B. 2 cm
C. 2.4 cm
D. 4.2 cm

4

A metallic hemisphere is melted and recast in the shape of a cone with the same base radius (R) as that of the hemisphere . If H is he height of the cone , then  :

A. H = 2R
B. H = 3R
C. H = `sqrt(3)R`
D. `H = 2/3 R`

5

A hemispherical bowl is filled to the brim with a beverage . The contents of the bowl any transferred into a cylindrical

vessel whose radius is 50% more than its height . If the diameter is same for both he bowl and the cylinder, the volume of the beverage in he cylindrical vessel is  :

A. `66 22/3`%
B. `78 1/2`%
C. 100%
D. More than 100 % (i.e., some liquid will be left in the bowl)