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? three circular bike mirror images with radii 4 cm, 7 cm, 8 cm respectively

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 \( A = l \times w \).

$$ A_{\text{rectangle}} = 10 \times 5 = 50 \, \text{cm}^2 $$

Step2: Recall area formula for circle

The area of a circle is \( A = \pi r^2 \), where \( r \) is the radius. We need to find which circular mirror (with given radii 4 cm, 7 cm, 8 cm) has an area approximately 50 \( \text{cm}^2 \).

Step3: Calculate area for radius 4 cm

For \( r = 4 \, \text{cm} \):

$$ A = \pi \times 4^2 = 16\pi \approx 16 \times 3.14 = 50.24 \, \text{cm}^2 $$

Step4: Calculate area for radius 7 cm

For \( r = 7 \, \text{cm} \):

$$ A = \pi \times 7^2 = 49\pi \approx 49 \times 3.14 = 153.86 \, \text{cm}^2 $$

Step5: Calculate area for radius 8 cm

For \( r = 8 \, \text{cm} \):

$$ A = \pi \times 8^2 = 64\pi \approx 64 \times 3.14 = 200.96 \, \text{cm}^2 $$

Answer:

The circular bike mirror with a radius of 4 cm (since its area \( \approx 50.24 \, \text{cm}^2 \) is approximately equal to the area of the old rectangular mirror, 50 \( \text{cm}^2 \)).