Question

8. First drop down menu answer choices A. Less than B. Equal to C greater than Second drop down answer choices A. 10 B. 20 C. 31.4 D. 15.7Third drop down answer choices A. 20 B. 10C. 31.4 D. 15.7

Answer 1

ANSWER and EXPLANATION

To find the person with the larger paper, we have to find the area of both pieces of paper.

Jada's paper is a rectangular-shaped paper that measures 5 inches by 4 inches.

To find the area of the paper, we have to find the product of its side lengths.

The area of Jada's paper is:

`\begin{gathered} A=5\cdot4 \\ A=20in^2 \end{gathered}`

Han's paper is shaped like the sector of a circle. The area of the sector of a circle is:

`A=(\theta)/(360)\cdot\pi r^2`

where θ = angle of the sector

r = radius

We have to find the measure of the angle of the sector by applying the formula for the length of an arc:

`\begin{gathered} L=(\theta)/(360)\cdot2\pi r \\ \Rightarrow2\pi=(\theta)/(360)\cdot2\pi\cdot5 \\ \Rightarrow\theta=(2\pi\cdot360)/(2\pi\cdot5) \\ \theta=72\degree \end{gathered}`

Hence, the area of Han's paper is:

`\begin{gathered} A=(72)/(360)\cdot\pi\cdot5^2 \\ A=15.7in^2 \end{gathered}`

As we can see, Jada's rectangular piece of paper has an area that is greater than Han's piece of paper shaped like a sector. The area of Jada's piece of paper is 20 in² and the area of Han's piece of paper is 15.7 in²