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 area of old mirror

The old mirror is a rectangle with length \( l = 10 \, \text{cm} \) and width \( w = 5 \, \text{cm} \). The area of a rectangle is \( A_{\text{rectangle}} = l \times w \). So, \( A_{\text{rectangle}} = 10 \times 5 = 50 \, \text{cm}^2 \).

Step2: Recall area formula for circle

The area of a circle is \( A_{\text{circle}} = \pi r^2 \), where \( r \) is the radius. We need to find the radius of the circle whose area is approximately \( 50 \, \text{cm}^2 \).

Step3: Solve for radius

Set \( \pi r^2 = 50 \). Using \( \pi \approx 3.14 \), we have \( 3.14 r^2 = 50 \). Then \( r^2 = \frac{50}{3.14} \approx 15.92 \), and \( r \approx \sqrt{15.92} \approx 4 \, \text{cm} \) (since \( 4^2 = 16 \), which is close to \( 15.92 \)).

Answer:

Reese should buy the circular bike mirror with a radius of 4 cm (the first one with the 4 cm radius).