Question

12. The diameter of all the circles is 6 cm. The circles are touching each other as shown
in the figure. Tind the area of shaded region.​

Answer 1

Given:

Diameter = 6 cm

To Find:

Area of the shaded

Explanation:

* See attached diagram.

We can see that the shaded part is made up by a circle and the enclosure made by the exterior of the 4 circles.

To find the enclosure, we will find the difference in the area of the square made by joining the centre of the 4 circles and 4 quadrants .

Find the radius:

$\text {Radius} = \text{Diameter} \div 2$

$\text {Radius} = 6 \div 2$

$\text {Radius} = 3 \text{ cm}$

Find the area of the circle:

$\text{Area of the circle} = \pi r^2$

$\text{Area of the circle} = \pi (3)^2$

$\text{Area of the circle} = 9\pi \text { cm}^2$

$\text {Area of the square} = 6 \times 6$

$\text {Area of the square} = 36 \text { cm}^2$

$\text {Area of the 4 quadrants} = 4 \bigg(\dfrac{1}{4} \times\pi (3)^2 \bigg)$

$\text {Area of the 4 quadrants} = 9\pi \text {cm}^2$

$\text{Area of the enclosure} = ( 36 - 9\pi ) \text { cm}^2$

Find the shaded area:

$\text{Shaded Area}= 9\pi + (36 - 9\pi)$

$\text{Shaded Area}= 9\pi + 36 - 9\pi$

$\text{Shaded Area}= 36 \text { cm}^2$

Answer: 36 cm²

Answer 2

Answer:

Please see the attachment