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 old mirror

The old mirror is a rectangle with length \( l = 10\space cm\) and width \( w=5\space cm\). Using the formula for the area of a rectangle \(A = l\times w\), we have \(A_{old}=10\times5 = 50\space cm^{2}\).

Step2: Calculate the area of the first circular mirror

The first circular mirror has a radius \(r = 4\space cm\). Using the formula for the area of a circle \(A=\pi r^{2}\), we get \(A_{1}=\pi\times4^{2}=16\pi\approx16\times 3.14 = 50.24\space cm^{2}\).

Step3: Calculate the area of the second circular mirror

The second circular mirror has a radius \(r = 7\space cm\). Using the formula \(A=\pi r^{2}\), we have \(A_{2}=\pi\times7^{2}=49\pi\approx49\times3.14 = 153.86\space cm^{2}\).

Step4: Calculate the area of the third circular mirror

The third circular mirror has a radius \(r = 8\space cm\). Using the formula \(A=\pi r^{2}\), we get \(A_{3}=\pi\times8^{2}=64\pi\approx64\times3.14 = 200.96\space cm^{2}\).

Answer:

The first circular mirror (with radius \(4\space cm\)) has an area approximately equal to the area of the old rectangular mirror. So Reese should buy the circular bike - mirror with a radius of \(4\space cm\).