Question

Alice cuts a circular piece of paper into sectors of equal sizes. She rearranges all sectors in a plane without gaps or overlaps with alternating curved parts. Which of these relates the area of the new arrangement to the area of the original whole piece of paper? idk how to post photos here but the link to then problem is https://prntscr.com/s1hkh6

Answer 1

Answer:

Option B.

Step-by-step explanation:

The complete question in the attached figure

we know that

The area of a circle is given by the formula

$A=\pi r^{2}$

we have that

Alice earranges all sectors in a plane without gaps or overlaps with alternating curved parts

That means ----> The area of the new arrangement must be equal to the area of the original whole piece of paper

The area of the original whole piece of paper is $\pi r^{2}$

therefore

The sectors form a parallelogram with a height of r and base πr .

Because

The area of the parallelogram is A=bh

we have

$b=\pi r\\h=r$

substitute

$A= \pi r(r)=\pi r^2$ ---> is the same that the area of the original whole piece of paper