ICSE Board Practice

Class VI Class VII Class VIII Class IX Class X
ICSE Grade X - Cone and Sphere
Question 1
1.
A hollow metallic cylindrical tube has an internal radius of 5.50 cm and height 16.00 cm. The thickness of the metal is 1 cm .The tube is melted to cast into a right circular cone of height 6.00 cm. Find the radius of the cone.
  • 10.80 cm
  • 7.80 cm
  • 11.80 cm
  • 9.80 cm
  • 8.80 cm
Question 2
2.
The radii of the ends of a frustum of a right circular cone 20.00 cm high are 7.00 cm and 4.00 cm. Its slant height is
  • 20.22 cm
  • 23.22 cm
  • 25.22 cm
  • 17.22 cm
  • 15.22 cm
Question 3
3.
A wooden toy rocket is in the shape of a cone mounted on a cylinder. The height of the conical part is 13.00 cm , while the height of the cylindrical part is 26.00 cm. The base of the conical portion has a diameter of 8.00 cm while the base diameter of the cylindrical portion is 4.00 cm. If the conical portion is painted with white and cylindrical portion with pink, find the area of the rocket painted with each of these colors
      • white
      • area =
      • 208.69 sq.cm
      • ,
      • pink
      • area =
      • 339.43 sq.cm
      • white
      • area =
      • 210.69 sq.cm
      • ,
      • pink
      • area =
      • 341.43 sq.cm
      • white
      • area =
      • 206.69 sq.cm
      • ,
      • pink
      • area =
      • 337.43 sq.cm
      • white
      • area =
      • 209.69 sq.cm
      • ,
      • pink
      • area =
      • 340.43 sq.cm
      • white
      • area =
      • 207.69 sq.cm
      • ,
      • pink
      • area =
      • 338.43 sq.cm
Question 4
4.
The radii of the ends of a frustum of a right circular cone 6.00 cm high are 6.50 cm and 3.50 cm. Its total surface area is
  • 397.11 sq.cm
  • 366.11 sq.cm
  • 388.11 sq.cm
  • 382.11 sq.cm
  • 354.11 sq.cm
Question 5
5.
From a circular cylinder of diameter 13.00 cm and height 10.00 cm, a conical cavity of the same base radius and of the same height is hollowed out. Find the volume of the remaining solid.
  • 885.24 cu.cm
  • 903.24 cu.cm
  • 909.24 cu.cm
  • 863.24 cu.cm
  • 869.24 cu.cm
Question 6
6.
If the slant height of a cone is 12.21 cm and T.S.A is 698.03 sq.cm, its L.S.A. is
  • 405.74 sq.cm
  • 369.74 sq.cm
  • 386.74 sq.cm
  • 383.74 sq.cm
  • 360.74 sq.cm
Question 7
7.
Two cubes each of volume 8000.00 cu.cm are joined end to end . Find the surface area of the resulting cuboid.
  • 4000.00 sq.cm
  • 4220.00 sq.cm
  • 3830.00 sq.cm
  • 3860.00 sq.cm
  • 4060.00 sq.cm
Question 8
8.
The radii of the ends of a frustum of a right circular cone 7.00 cm high are 9.50 cm and 6.00 cm. Its volume is
  • 1593.83 cu.cm
  • 1483.83 cu.cm
  • 1343.83 cu.cm
  • 1173.83 cu.cm
  • 1263.83 cu.cm
Question 9
9.
A solid consists of a cylinder with two hemispherical ends with length 26.00 cm and diameter 11.00 cm. Find the total surface area of the solid
  • 1039.14 sq.cm
  • 1499.14 sq.cm
  • 1299.14 sq.cm
  • 1129.14 sq.cm
  • 1279.14 sq.cm
Question 10
10.
If the vertical height of a cone is 5.00 cm and volume is 335.24 cu.cm, its slant height is
  • 10.43 cm
  • 9.43 cm
  • 8.43 cm
  • 11.43 cm
  • 7.43 cm