1 
Find the volume of the largest sphere which can be cut from a cube having edges of 7 cm length. Appr...
CAT
Quantitative Ability
Geometry
Mensuration

2 
A telephone company places round cables in round ducts. Assuming the diameter of a cable is 2 cm, wh...
CAT
Quantitative Ability
Geometry
Mensuration
Spheres and Hemispheres

3 
An equilateral triangle has a side of 12 cm. Find the area (in sq. cm) formed by the incentre, centr...
CAT
Quantitative Ability
Geometry
Mensuration

4 
A conical cup when completely filled with ice cream forms a hemispherical shape on its open end. Fin...
CAT
Quantitative Ability
Geometry
Mensuration

5 
A metallic solid cylinder of 14 cm diameter and 32 cm height is cast into 77 solid cubes of equal si...
CAT
Quantitative Ability
Geometry
Mensuration

6 
A right circular cone is cut parallel to its base at one third of its height from the top. Find the ...
CAT
Quantitative Ability
Geometry
Mensuration

7 
A circular sheet of paper of radius 6 cm is cut into six equal sectors. Each sector is formed i...
CAT
Quantitative Ability
Geometry
Mensuration

8 
A swimming pool 150 m long and 50 m wide is 1 m deep at the shallow end and 6 m deep at the deep end...
CAT
Quantitative Ability
Geometry
Mensuration

9 
A vessel is in the form of an inverted cone.Its depth is 8 cm and the diameter of its top, which is ...
CAT
Quantitative Ability
Geometry
Mensuration

10 
A cuboid of dimension 24cm * 9 cm * 8cm is melted and smaller cubes are of side 3 cm is formed....
CAT
Quantitative Ability
Geometry
Mensuration

11 
A conical tent is to accommodate 10 persons. Each person must have 6 m2 space to sit and 3...
CAT
Quantitative Ability
Geometry
Mensuration

12 
A cylindrical vessel of diameter 48 cm has water to a height of 10 cm. A metal cube of 14 cm edge is...
CAT
Quantitative Ability
Geometry
Mensuration

13 
The areas of three adjacent faces of a cuboid are x, y, z. If the volume is V,then V2 will be equal ...
CAT
Quantitative Ability
Geometry
Mensuration

14 
In the square below, each vertex is joined to the midpoint of the opposite sides and a star shape is...
CAT
Quantitative Ability
Geometry
Mensuration

15 
A solid wood toy is in the shape of a right circular cone mounted on a hemisphere. If the radiu...
CAT
Quantitative Ability
Geometry
Mensuration

16 
Three balls are placed inside a cone such that each ball is in contact with the edge of the cone and...
CAT
Quantitative Ability
Geometry
Mensuration
Cones and Cylinders

17 
The area of the four walls of a room is 660 m2 and its length is twice its breadth. If its height is...
CAT
Quantitative Ability
Geometry
Mensuration
Cubes and Cuboids

18 
Three cubes each of volume of 216 m3 are joined end to end. Find the surface area of the resulting f...
CAT
Quantitative Ability
Geometry
Mensuration

19 
Two circles of radii 9 cm and 4 cm touch each other externally. Find the length of their direct comm...
CAT
Quantitative Ability
Geometry
Mensuration

20 
If one angle of a pentagon is 40o and all the other angles are equal, find the measure of each ...
CAT
Quantitative Ability
Geometry
Mensuration

21 
A roller is 8 m long and has a diameter of 0.7 m. It takes exactly 1000 rotations of the roller to l...
CAT
Quantitative Ability
Geometry
Mensuration

22 
A rectangle and an equilateral triangle with equal area are inscribed in a circle with radius, 2. ...
CAT
Quantitative Ability
Geometry
Mensuration
