Question

a rectangular piece of paper with length 39 cm and width 18 cm has two semicircles cut out of it, as shown below. find the area of the paper that remains. use the value 3.14 for π, and do not round your answer. be sure to include the correct unit in your answer.

Explanation:

Step1: Calculate area of rectangle

The area formula for a rectangle is $A = l\times w$, where $l = 39$ cm and $w = 18$ cm. So $A_{rectangle}=39\times18 = 702$ $cm^{2}$.

Step2: Calculate area of two - semi - circles (one full - circle)

The diameter of the circle is equal to the width of the rectangle, so $d = 18$ cm and $r=\frac{d}{2}=\frac{18}{2}=9$ cm. The area formula for a circle is $A=\pi r^{2}$. Using $\pi = 3.14$ and $r = 9$ cm, we have $A_{circle}=3.14\times9^{2}=3.14\times81 = 254.34$ $cm^{2}$.

Step3: Calculate remaining area

The remaining area $A_{remaining}=A_{rectangle}-A_{circle}$. So $A_{remaining}=702 - 254.34=447.66$ $cm^{2}$.

Answer:

$447.66$ $cm^{2}$