3 circles each of radius 3.5 cm are drawn in such a way that each of them touches the other two . find the area enclosed between these three cicles (shaded region )use pie=22/7?
If we try to draw the figure as per the given the question, then it will look like this :-
Ignore the measurements
Area of the shaded region = Area of equilateral triangle - Areas of 3 sectors of 60 at vertices of triangle
= rt.3/ 4 * 7 * 7 - (3 * 60/360 * 22/7 * 3.5 * 3.5) (side of equi. tri = 3.5 +3.5 = 7 cm )
= 49 rt3 / 4 - (11*5*35) /100
= 84.868/4 - 1925/100
= 21.217 - 19.25 = 1.967 cm2
Hope it helps !
Plz. thumbs up.
If the circles just touch each other, then you can draw a line connecting the centres of each pair of adjacent circles creating an equilateral triangle of side length 7 (2 times 3.5). The area of an equilateral triangle is given by:
There are four areas inside of this equilateral triangle, three circle sectors and the area we seek.
The area of a circle sector is given by:
where is the central angle of the sector.
So, the area we want is the area of the equilateral triangle minus three times the sector area.
You just need to simplify but I would leave the answer in terms of the radical and