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Shailja Chauhan

· started a discussion

· 1 Months ago

area of sector (Question: 16225.0 )

area of sector = 1/3 * pai * rsquare

Question:
There is an equilateral triangle of which each side is 2 meter with all the three corners as centres circles are described each of radius 1 meter. The total common area to all circles and the triangle is?
Options:
A) 23.09 sq.meter.
B) 2.53 sq.meter.
C) 17.04 sq.meter.
D) 1.57 sq.meter.
E) None of these.
Solution:
We know that

the side of the equilateral triangle is double the radius of circle. 

let r be the radius of circle

therefore, 

Area of each sector = \({1 \over 6}*\pi * r^2\)

therefore,  Area of common to all circle and triangle = 

\(3* {1 \over 6}*\pi r^2={1 \over 2}\pi r^2\)

= \({1 \over 2}*{22 \over 7}*1=1.57sq.m\)

kanhaiya jha

· commented

· 1 Months ago

angle of equilateral triangle is 60 degrees and angle at centre of triangle is 360 degrees. Hence,

area of sector = 1/6 * pi * r^2
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