Answered

Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

Below is the justification for the formula for the area of a circle. Which word, when placed in the blank, best completes this argument?

- The circumference of a circle is given by the formula [tex]$C=2 \pi r$[/tex] where [tex]$r$[/tex] is the radius.
- If the circle is divided into equally sized sectors, the sectors can be rearranged to form a shape that approximates a parallelogram.
- The base of the parallelogram is half the circumference, or [tex][tex]$\pi r$[/tex][/tex], and the height is \_\_\_\_\_.
- Because the area of a parallelogram is equal to the product of the base and the height, the area is [tex]$\pi r^2$[/tex].
- Therefore, the area of a circle is given by the formula [tex]$\pi r^2$[/tex].

Which word best completes the blank?

Sagot :

GinnyAnswer
To complete the argument correctly, the blank should be filled with the term "the radius," because the height of the parallelogram formed by rearranging the circle's sectors is equivalent to the radius of the circle. Here's the complete argument with the blank filled:

- The circumference of a circle is given by the formula [tex]\(C = 2 \pi r\)[/tex], where [tex]\(r\)[/tex] is the radius.
- If the circle is divided into equally sized sectors, the sectors can be rearranged to form a shape that approximates a parallelogram.
- The base of the parallelogram is half the circumference, or [tex]\(\pi r\)[/tex], and the height is the radius.
- Because the area of a parallelogram is equal to the product of the base and the height, the area is [tex]\(\pi r \times r = \pi r^2\)[/tex].
- Therefore, the area of a circle is given by the formula [tex]\(\pi r^2\)[/tex].
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.