Answered

At Westonci.ca, we provide reliable answers to your questions from a community of experts. Start exploring today! Explore our Q&A platform to find in-depth answers from a wide range of experts in different fields. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

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

[tex]undefined[/tex]

Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We appreciate your time. Please come back anytime for the latest information and answers to your questions. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.