CAT Mensuration Problems and Solutions: Mensuration Questions you should solve for CAT Prep

CAT Mensuration Practice Exercise-2

Geometry and Mensuration is one of the most important sections in Quantitative Analysis part of CAT. Many students have the wrong perception that geometry and mensuration problems are tough to crack. This is not completely true. With the help of these tests and examples you will be able to cruise through the section easily. Remember, the purpose of these CAT mensuration problems and solutions is to provide you relevant examples and practice material that helps you understand the subtle nuances for the topic.

Question 1: Three identical cones with base radius are placed on their bases so that each in touching the other two. The radius of the circle drawn through their vertices is:

(a) Smaller than
(b) Equal to
(c) Larger than
(d) Depends on the height of the cones

Question 2: A slab of ice 8 inches in length, 11 inches in breadth, and 2 inches thick was melted and re-solidified in the form of a rod of 8 inches diameter. The length of such a rod, in inches, in nearest to:

(a) 3
(b) 3·5
(c) 4
(d) 4·5

Question 3: A right circular cone of height h is cut by a plane parallel to the base at a distance h/3 from the base, then the volumes of the resulting cone and the frustum are in the ratio :

(a) 1: 3
(b) 8: 19
(c) 1: 4
(d) 1: 7

Question 4: The length of a ladder is exactly equal to the height of the wall it is leaning against. The lower end of the ladder is kept on a stool of height 3 m and the stool is kept 9 m away from the wall, the upper end of the ladder coincides with the top of the wall. Then, the height of the wall is:

(a) 12 m
(b) 15 m
(c) 18 m
(d) 11 m

Question 5: In the adjoining figure, AC +AB = 5AD and AC – AD = 8. Then, the area of the rectangle ABCD is:

(a) 36
(b) 50
(c) 60
(d) Cannot be answered

Extra tips for CAT Mensuration Problems and Solutions:

• Revise the formulas and concepts of mensuration from 10th standard textbooks. Try to remember all the formulas based on different shapes and different parameters.
• Try to find common terms in formulas and understand their use as it makes it easier to memorize.
• Drawing diagrams after analyzing the problem is the most important step in solving any geometry related question, especially CAT Mensuration problems and solutions.
• Understand which parameters are to be found out and apply the formulas accordingly.
• Brush up the basic concepts and properties of every shape as this helps to simplify the solution further.
• Revise the basic theorems and angle properties along with the formulas.