Question

dominic needs a new bike mirror. his old mirror was a square with a side length of 9 cm. he wants the new mirror to have an area as close as possible to his old bike mirror. which circular bike mirror should dominic buy?

Explanation:

Step1: Calculate area of old square mirror

The area formula for a square is $A = s^2$, where $s = 9$ 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: Compare areas

We want to find the circular mirror with an area closest to 81 $cm^2$.
$|81 - 200.96|=119.96$, $|81 - 153.86| = 72.86$, $|81 - 78.5|=2.5$.

Answer:

The circular bike mirror with a radius of 5 cm.