Question

the diameter of the mirror with the frame is 17 inches. to the nearest hundredth, what is the area of only the frame? use 3.14 for π. enter the correct answer in the box.

Explanation:

Step1: Find radius of mirror

The mirror has a diameter of 15 inches, so its radius is half the diameter.
$r_m = \frac{15}{2} = 7.5$ in

Step2: Find radius of mirror + frame

The total diameter (mirror + frame) is 17 inches, so its radius is half this value.
$r_t = \frac{17}{2} = 8.5$ in

Step3: Calculate area of mirror

Use the circle area formula $A = \pi r^2$ for the mirror.
$A_m = 3.14 \times (7.5)^2 = 3.14 \times 56.25 = 176.625$ in²

Step4: Calculate area of mirror + frame

Use the circle area formula for the total area.
$A_t = 3.14 \times (8.5)^2 = 3.14 \times 72.25 = 226.865$ in²

Step5: Subtract to find frame area

Subtract the mirror area from the total area to get the frame's area.
$A_f = 226.865 - 176.625 = 50.24$ in²

Answer:

50.24 square inches