Question

Three equal circles,each of radius 6 cm, touch one another. Find the area enclosed between them (Take pi=3.14 &root3=1.732)​

Answer 1

Answer: 5.832 cm²

Step-by-step explanation: Join the centres of all the circles

U get an equilateral triangle ABC of each length 12 cm .

Draw a perpendicular from C which cuts AB at D.

Area of an equilateral triangle can be found if we know the side length

The formula is $\frac{\sqrt{3} }{4} a^{2}$ where a is the side i.e. in this case , 12 cm

∴$\frac{\sqrt{3} }{4} 12^{2}$ = $\frac{1.732 * 144}{4}$ = 62.352 cm²

To find the area enclosed, (in my picture it's the red shaded region) we have to subtract the areas of the 3 green sectors .

Since the angles of an equilateral triangle is 60° , one green sector has 1/6th area of the circle .

Area of a circle = $\pi r^{2}$ , 3.14 x 36 = 113.04 cm²

Area of a sector = 113.04/6 = 18.84 cm²

∴ Area of 3 sectors = 18.84 x 3 = 56.52 cm²

∴ Area of the red shaded region = 62.352 - 56.52 = 5.832 cm²

Answer 2

Step-by-step explanation:

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