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

Explanation:

Step1: Calculate old mirror area

The old mirror is a rectangle, so use area formula $A = l \times w$.
$A = 10\ \text{cm} \times 5\ \text{cm} = 50\ \text{cm}^2$

Step2: Calculate area of 4cm mirror

Use circle area formula $A = \pi r^2$, take $\pi \approx 3.14$.
$A = 3.14 \times (4\ \text{cm})^2 = 3.14 \times 16 = 50.24\ \text{cm}^2$

Step3: Calculate area of 7cm mirror

$A = 3.14 \times (7\ \text{cm})^2 = 3.14 \times 49 = 153.86\ \text{cm}^2$

Step4: Calculate area of 8cm mirror

$A = 3.14 \times (8\ \text{cm})^2 = 3.14 \times 64 = 200.96\ \text{cm}^2$

Step5: Match area to old mirror

Compare calculated areas to $50\ \text{cm}^2$.

Answer:

Reese should buy the circular bike mirror with a radius of 4 cm, as its area ($50.24\ \text{cm}^2$) is approximately equal to the area of her old rectangular mirror ($50\ \text{cm}^2$).