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? .

(a) 2/cm

(b) 3/cm

(c) 6/cm

(d) 9/cm

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 cm^{3}

(b) 1200 cm^{3}

(c) 1848 cm^{3}

(d) 2400 cm^{3}

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 cm^{3})? .

(a) 1441

(b) 3808

(c) 3308

(d) 3880

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) 2m

(b) 3m

(c) 4m

(d) 5m

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) 2473cu.cm

(b) 2963cu.cm

(c) 3213cu.cm

(d) 3593cu.cm

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 .

(a) 40%

(b) 72.8% .

(c) 86.4% .

(d) 400%

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 cm^{3}

(b) 1092 cm^{3}

(c) 462 cm^{3}

(d) 362 cm^{3}

The volume of a right circular cone is 196p cm^{3}. If the area of its base is 154 cm^{2},
what is the vertical height of the cone? .

(a) 10 cm

(b) 12 cm

(c) 14 cm

(d) 16 cm

1.B. |
2.C. |
3.A. |
4.D. |
5.C. |

6.D. |
7.B. |
8.B. |
9.C. |
10.B. |