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Find the area of the shaded sector it the radius of the circle is 1.5

Find The Area Of The Shaded Sector It The Radius Of The Circle Is 15 class=

Sagot :

We are given a circle with a radius equal to 15

We know that a full-circle corresponds to 360°.

Whereas a semi-circle corresponds to 180°.

So, the angle corresponding to the shaded region can be found as

[tex]180\degree-45\degree=135\degree[/tex]

Now we can use the following formula to find the area of the shaded sector.

[tex]A=\frac{\theta\times\pi}{360\degree}\times r^2[/tex]

Where r is the radius of the circle and θ is the angle of the shaded sector (that is 135°)

Let us substitute the given values into the above formula to get the area of the shaded sector.

[tex]\begin{gathered} A=\frac{135\degree\times\pi}{360\degree}\times15^2 \\ A=\frac{3\pi}{8}\times225 \\ A=\frac{675\pi}{8} \\ A=265.07 \end{gathered}[/tex]

Therefore, the area of the shaded sector is 265

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