When a cubical metallic piece of edge 3 cm is
dropped in a cylindrical glass of water, the water column rises by 3 cm. What
is the radius of the base of the glass? .
The diameter of the base of a cylinder is 14
cm and its height is 12 cm. What is the volume of the cylinder? .
(a) 1600 cm3
(b) 1200 cm3
(c) 1848 cm3
(d) 2400 cm3
The volumes of two cones are in the ratio of
1 : 10 and the radii of the cones are in the ratio of 1 : 2, what is the ratio
of their vertical heights?
(a) 2 : 5
(b) 1 : 5
(c) 3 : 5
(d) 4 : 5
A sphere of the maximum possible volume is
carved out of a cubical wooden block of edge 42 cm. What is the volume of the
sphere carved (in cm3)? .
A hemispherical tank of inner radius 7 m is
completely filled with water. A pipe attached at the bottom of the tank is
opened and the water is made to completely flow into a cylindrical tank of base
radius 7 m. The height to which the water level in the cylindrical tank rises
is _______. .
A frustum is formed by cutting a right
circular cone such that the radius of the upper face is 7 cm and the radius of
the lower face is 14 cm, and the height of the frustum is 10 cm. The volume of
the frustum is .
A metallic sphere of radius 21 m is melted
and formed as a cylinder of 14 m diameter. What is the length of the cylinder? .
(a) 126 m
(b) 252 m
(c) 504 m
(d) 1008 m
The radius of the base of a right circular
cone and the height of the cone are increased by 20% each. The percentage
increase in the volume of the cone is .
(b) 72.8% .
(c) 86.4% .
A rectangular sheet of metal is 28 cm by 13
cm. Equal squares of side 3 cm are cut off at the corners and the remainder is
folded up to form an open rectangular box. What is the volume of this box? .
(a) 231 cm3
(b) 1092 cm3
(c) 462 cm3
(d) 362 cm3
The volume of a right circular cone is 196p cm3. If the area of its base is 154 cm2,
what is the vertical height of the cone? .
(a) 10 cm
(b) 12 cm
(c) 14 cm
(d) 16 cm