Mensuration Questions Answers

Mensuration - Quant/Math - CAT 2008

Question 4 the day: May 29, 2003

The question for the day is from the topic of Mensuration.

Four horses are tethered at 4 corners of a square field of side 70 metres so that they just cannot reach one another. The area left ungrazed by the horses is:

(1)	1050 sq.m			(2)	3850 sq.m
(3)	950 sq.m			(4)	1075 sq.m

Correct Answer - (1)

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Solution:


The length of the rope in which the horses tied should be equal to half of the side of the square plot so that they just cannot reach one another.

Therefore, the length of the rope is 35m (70/2).

The area covered by each horse should be equal to the area of sector with radius of 70/2 = 35m(length of the rope).

Total area covered by the four horses = 4* area of sector of radius 35 metres = Area of circle of radius 35m.

Area left ungrazed by the horses = Area of square field - Area covered by four horses.

= 70² - (22/7)*35*35 = 4900 - 3850 = 1050 sq.m.