Three coins of radius 2 cm each are kept on a table such that each touches the other two find area of the space bounded by the coins in Sq cm
Answers
Answer:
add the area of three circle by :- 2πr2
The area of the space bounded by the three coins each of radius 2 cm is 0.648 cm².
Step-by-step explanation:
It is given that 3 coins each of radius 2 cm are kept on the table in such a way that each touches the other two.
Join the centres of each circle. (As shown in the figure attached below)
We get a ΔABC after joining the centres.
Since the radius of each circle is 2 cm
∴ Each side of the triangle, a = AB = BC = CA = 2+2 = 4 cm
⇒ ∠A = ∠B = ∠C = 60° i.e., ∆ABC is an equilateral triangle.
Now,
The area of the equilateral ∆ ABC = (√3/4) * a² = (√3/4) * 4² = 4√3 cm²
And,
The area of the 3 sectors is given by,
= 3 * [πr² * (θ/360°)]
= 3 * [(22/7) * 2² * (60°/360°)]
= 3 * [(22/7) * 4 * (1/6)]
= 6.28 cm²
Thus,
The area of the space bounded by the coins is given by,
= [area of the equilateral ∆ABC] – [area of the 3 sectors]
= 4√3 – 6.28
= 6.928 – 6.28
= 0.648 cm²
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