dominic needs a new bike mirror. his old mirror was a square with a side length of 9 cm. he wants the new…

Explanation:

Step1: Calculate area of square mirror

The area formula for a square is $A = s^2$, where $s$ is the side - length. Given $s = 9$ cm, so $A_{square}=9^2=81$ $cm^2$.

Step2: Calculate areas of circular mirrors

The area formula for a circle is $A=\pi r^2$. For the first circular mirror with $r = 8$ cm, $A_1=\pi\times8^2=64\pi\approx64\times3.14 = 200.96$ $cm^2$. For the second circular mirror with $r = 7$ cm, $A_2=\pi\times7^2 = 49\pi\approx49\times3.14=153.86$ $cm^2$. For the third circular mirror with $r = 5$ cm, $A_3=\pi\times5^2=25\pi\approx25\times3.14 = 78.5$ $cm^2$.

Step3: Find the closest - area circular mirror

We find the absolute differences: $|A_1 - A_{square}|=|200.96 - 81| = 119.96$ $cm^2$. $|A_2 - A_{square}|=|153.86 - 81| = 72.86$ $cm^2$. $|A_3 - A_{square}|=|78.5 - 81|=2.5$ $cm^2$. Since 2.5 is the smallest difference, the circular mirror with radius 5 cm is the closest in area to the square mirror.

Answer:

The circular bike mirror with a radius of 5 cm.