Question

you want to cut a 4-foot-wide circle out of an 8 by 12-foot rectangle of sheet metal. how many square feet of sheet metal will be left over after removing the circle?

Explanation:

Calculate the area of the rectangle

Find the total area of the sheet metal.

$$ A_{\text{rectangle}} = \text{length} \times \text{width} = 12 \times 8 = 96\text{ sq ft} $$

Find the radius of the circle

The circle is 4 feet wide, meaning its diameter is 4 feet.

$$ r = \frac{d}{2} = \frac{4}{2} = 2\text{ ft} $$

Calculate the area of the circle

Find the area of the circle using \(\pi \approx 3.14\).

$$ A_{\text{circle}} = \pi r^2 \approx 3.14 \times 2^2 = 3.14 \times 4 = 12.56\text{ sq ft} $$

Calculate the remaining area

Subtract the circle's area from the rectangle's area.

$$ A_{\text{left}} = A_{\text{rectangle}} - A_{\text{circle}} = 96 - 12.56 = 83.44\text{ sq ft} $$

Answer:

\(83.44\text{ sq ft}\) (or \(96 - 4\pi\text{ sq ft}\))