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A sector with a central angle measure of \purpleD{\dfrac{\pi}{6}} 6π start color #7854ab, start fraction, pi, divided by, 6, end fraction, end color #7854ab (in radians) has a radius of \maroonD{12\,\text{cm}}12cmstart color #ca337c, 12, start text, c, m, end text, end color #ca337c.

A Sector With A Central Angle Measure Of PurpleDdfracpi6 6π Start Color 7854ab Start Fraction Pi Divided By 6 End Fraction End Color 7854ab In Radians Has A Rad class=

Sagot :

EXPLANATION:

Given;

We are given a sector of a circle with the following dimensions;

[tex]\begin{gathered} radius=12 \\ central\text{ }angle=\frac{\pi}{6} \end{gathered}[/tex]

Required;

We are required to calculate the area of the sector with the details given.

Step-by-step solution;

To calculate the area of a sector with the central angle given in radians, we will use the following formula;

[tex]Area\text{ }of\text{ }a\text{ }sector=\frac{\theta}{2\pi}\times\pi r^2[/tex]

We can now substitute and solve;

[tex]Area=\frac{\frac{\pi}{6}}{2\pi}\times\pi r^2[/tex][tex]Area=(\frac{\pi}{6}\div\frac{2\pi}{1})\times\pi r^2[/tex][tex]Area=(\frac{\pi}{6}\times\frac{1}{2\pi})\times\pi\times12^2[/tex][tex]Area=\frac{1}{12}\times144\times\pi[/tex][tex]Area=12\pi[/tex]

ANSWER:

In terms of pi the area of the sector is

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