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In the diagram, the radius of the outer circle is 2x em and the radius of the inside circle is 6 cm. The area of the shaded region is 220 cm? What is the value of x2​

In The Diagram The Radius Of The Outer Circle Is 2x Em And The Radius Of The Inside Circle Is 6 Cm The Area Of The Shaded Region Is 220 Cm What Is The Value Of class=

Sagot :

elcharly64

Answer:

Answer: 8 (second choice)

Step-by-step explanation:

Area of a Circle

Given a circle of radius r, the area is calculated by the formula:

[tex]A=\pi\ r^2[/tex]

There are two circles in the diagram. The outer circle has a radius of r1=2x, thus its area is:

[tex]A_1=\pi\ (2x)^2[/tex]

The interior circle has a radius of r2=6 cm, thus its area is:

[tex]A_2=\pi\ 6^2=36\pi[/tex]

The shaded area is obtained by subtracting A1-A2:

[tex]A=\pi\ (2x)^2-36\pi[/tex]

The value of the shaded area is given as 220π cm2. Equating:

[tex]\pi\ (2x)^2-36\pi=220\pi[/tex]

Dividing by π:

[tex](2x)^2-36=220[/tex]

Adding 36:

[tex](2x)^2=220+36=256[/tex]

Taking square root:

[tex]2x=\sqrt{256}=16[/tex]

Dividing by 2:

x = 8 cm

Answer: 8 (second choice)

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