Question

challenge 11 the diagram shows a rectangular piece of pastry with eight circles cut out. the diameter of each circle is 8cm. what is the area of the pastry that is left? give your answer correct to three significant figures (3 s.f.).
diagram of a rectangle labeled 37cm (height) and 20cm (width) with eight circles inside

Explanation:

Step1: Calculate area of rectangle

The formula for the area of a rectangle is \( A = l \times w \), where \( l = 37 \, \text{cm} \) and \( w = 20 \, \text{cm} \).
\( A_{\text{rectangle}} = 37 \times 20 = 740 \, \text{cm}^2 \)

Step2: Calculate radius of one circle

The diameter of each circle is \( 8 \, \text{cm} \), so the radius \( r = \frac{8}{2} = 4 \, \text{cm} \).

Step3: Calculate area of one circle

The formula for the area of a circle is \( A = \pi r^2 \).
\( A_{\text{circle}} = \pi \times 4^2 = 16\pi \, \text{cm}^2 \)

Step4: Calculate total area of 8 circles

\( A_{\text{8 circles}} = 8 \times 16\pi = 128\pi \, \text{cm}^2 \approx 128 \times 3.1416 = 402.1248 \, \text{cm}^2 \)

Step5: Calculate area of remaining pastry

Subtract the total area of the circles from the area of the rectangle.
\( A_{\text{remaining}} = 740 - 402.1248 = 337.8752 \, \text{cm}^2 \)

Step6: Round to three significant figures

\( 337.8752 \approx 338 \, \text{cm}^2 \) (to three significant figures)

Answer:

\( 338 \, \text{cm}^2 \)