Question

1. 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.40 which circular bike mirror should reese buy?

Explanation:

Step1: Calculate old mirror area

Area of rectangle: $A_{rect} = l \times w = 10 \times 5 = 50$ cm²

Step2: Calculate area of 4cm mirror

Area of circle: $A_{circle} = \pi r^2$
$A_1 = \pi \times 4^2 = 16\pi \approx 50.27$ cm²

Step3: Calculate area of 7cm mirror

$A_2 = \pi \times 7^2 = 49\pi \approx 153.94$ cm²

Step4: Calculate area of 8cm mirror

$A_3 = \pi \times 8^2 = 64\pi \approx 201.06$ cm²

Step5: Match to closest area

Compare $50.27$, $153.94$, $201.06$ to $50$ cm².

Answer:

Reese should buy the circular bike mirror with a radius of 4 cm.