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# Problems on Mensuration: CAT Quantitative Aptitude

May 25, 2012 17:21 IST

This article takes you through some application based problems on the topic of Mensuration. Mensuration is a topic which has many formulaes in it. Let’s look at some solved problems.

Example:

A rectangle of   length ‘a’ and width ‘b’ is rolled about its length. The volume of the resulting cylinder is:

Solution:

If we roll a rectangle of length a and width b about its length, we get a cylinder as shown above.
The height of the resultant cylinder is ‘b’ and the length ‘a’ = 2R

R (if we were to compare the length changing into the circumference of the circle at the cylinder’s end.

Therefore, by implication, volume of cylinder can be found as shown below.

Hence, the correct option is [3].

Example:

From a plate in the shape of an equilateral triangle, three symmetrical sections are cut as shown. What percentage of the plate is wasted?

Solution:

We can find the area of ΔAPQ, which will be =

Side of equilateral triangle = 2a.

Hence, the correct option is [1].

Example:

Two circles of 5 cm each intersect each other as shown in the figure. The area of the overlapping (shaded) regions so formed is:

Solution:

It is the same as the shaded area shown here x 2.

Area of the triangle =

Area of the sector =

Area of overlapping portion =

Hence, the correct option is [2].

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