Question

topic: circles
progress:
the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.
question id: m2x06
find the area to the nearest square foot of the shaded region below, consisting of a square with a circle cut out of it. use 3.14 as an approximation for $pi$.
14 ft
$\bigcirc$ 154 square feet
$\bigcirc$ 105 square feet
$\bigcirc$ 42 square feet
$\bigcirc$ 419 square feet

Explanation:

Step1: Calculate square area

The square's side equals the circle's diameter (14 ft).
Area of square: $14 \times 14 = 196$ square feet

Step2: Calculate circle radius

Radius is half the diameter.
$r = \frac{14}{2} = 7$ ft

Step3: Calculate circle area

Use $\pi=3.14$, area formula $\pi r^2$.
Area of circle: $3.14 \times 7^2 = 3.14 \times 49 = 153.86$ square feet

Step4: Find shaded area

Subtract circle area from square area.
$196 - 153.86 = 42.14$ square feet

Step5: Round to nearest whole number

$42.14 \approx 42$ square feet

Answer:

42 square feet