Question

In this diagram,

Answer 1

The area of the smallest circle with radius 3 is 28.27 unit². The area of the yellow ring and white ring is 28.27 unit² and 56.55 unit².

What is the area of the circle?

The area of the circle is the space occupied by it. It can be given as,

$A=\pi r^2$

Here (r) is the radius of the circle.

In this diagram, three concentric circles' rectangle.

• Point C lies in the middle have their centers at O, and OABC is a lies on the outer circle.
• Point A lies on the inner circle, and point B the smallest circle.

• 1. The area of the smallest circle-

The radius of the smallest circle is 3.

$r_1=3\rm\unit$

Thus, the area of it is,

$A=\pi (3)^2\\A=28.27\rm\; unit^2$

• 2. The area of the yellow ring.

Let suppose the mid-point of the rectangle is D. Here, OB is the diagonal of the rectangle in which,

$OD=BD$  

The radius of the yellow ring's outer face from point O is,

$r_3=OD+BD\\r_3=OD+OD\\r_3=2OD$

OD is the radius of the small circle, which is 3 units long. Thus,

$r_3=2\times3\\r_3=6\rm\; units$

The line segment OC is the radius of the white circle from point O. In the triangle COB from the Pythagoras theorem, the radius r₂ of the middle circle is,

$r_2=\sqrt{r_3^2-r_1^2}\\r_2=\sqrt{6^2-3^2}\\r_2=3\sqrt3$

Thus, the area of the yellow ring is,

$A_y=\pi r_3^2-\pi r_2^2\\A_y=\pi (6)^2-\pi (3\sqrt{3})^2\\A_y=28.27\rm\; unit^2$

• 3. The area of the white ring.

The area of white ring is,

$A_w=\pi r_2^2-\pi r_1^2\\A_w=\pi (3\sqrt{3})^2-\pi (3)^2\\A_w=56.55\rm\; unit^2$

Hence, the area of the smallest circle with radius 3 is 28.27 unit². The area of the yellow ring and white ring is 28.27 unit² and 56.55 unit².

Learn more about the area of the circle here;

brainly.com/question/402655

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