Question

Three circles each of radius 7 cm are drawn in such a way that each of their touches the outer to find the area enclosed between the circles

Answer 1

Answer:

Step-by-step explanation:

Hope it helps.....

Answer 2

Given:

Three circles each of radius 7 cm are drawn in such a way that each of them touches the outer

To Find:

find the area enclosed between the circles

Solution:

We should know the formula for the area of an equilateral triangle and the area of a sector of a circle,

The area of an equilateral triangle is,

$Area=\frac{\sqrt{3} }{4}a^2$

And the area of a sector of a circle is,

$Area=\pi r^2\frac{\theta}{360}$

We should know that by joining the three centres we will form an equilateral triangle with sides of 7+7=14cm and three sectors on each vertex whose radius is 7 cm so the area of the enclosed part will be the area of the equilateral triangle minus the area of the three sectors,

So,

$Area=\frac{\sqrt{3} }{4}a^2-\pi r^2\frac{\theta}{360}\\=\frac{\sqrt{3} }{4}14^2-\pi 7^2\frac{60}{360}\\\\=49\sqrt{3} -77\\=7.87cm^2$

Hence, the area of the enclosed part is 7.87cm^2.