Question

reese needs a new bike mirror. her old mirror was a rectangle with a length of 10 cm and a width of 5 cm. she wants the new mirror to have approximately the same area as the old mirror. which circular bike mirror should reese buy?

Explanation:

Step1: Calculate the area of the rectangular mirror

The area formula for a rectangle is $A = l\times w$. Given $l = 10$ cm and $w = 5$ cm, so $A_{rectangle}=10\times5 = 50$ $cm^{2}$.

Step2: Calculate the areas of the circular mirrors

The area formula for a circle is $A=\pi r^{2}$.
For $r = 4$ cm, $A_1=\pi\times4^{2}=16\pi\approx16\times3.14 = 50.24$ $cm^{2}$.
For $r = 7$ cm, $A_2=\pi\times7^{2}=49\pi\approx49\times3.14 = 153.86$ $cm^{2}$.
For $r = 8$ cm, $A_3=\pi\times8^{2}=64\pi\approx64\times3.14 = 200.96$ $cm^{2}$.
The circular mirror with a radius of 4 cm has an area closest to the area of the rectangular mirror.

Answer:

The circular bike - mirror with a radius of 4 cm.