QuestionA rondavel (hut / circular dwelling) has a square woven carpet covering the floor as shown in the diagram below. The circumference of the rondavel is 113,1 metres.
Calculate the area of the floor which is not covered by the carpet.

Studdy Solution
Calculate the area of the floor not covered by the carpet:
$$A_{\text{uncovered}} = A_{\text{circle}} - A_{\text{square}}$$
Substitute the areas from Steps 2 and 4:
$$A_{\text{uncovered}} = \pi r^2 - 2r^2$$ $$= r^2(\pi - 2)$$
Substitute the radius from Step 1:
$$r = \frac{113.1}{2\pi}$$
$$A_{\text{uncovered}} = \left(\frac{113.1}{2\pi}\right)^2 (\pi - 2)$$
Calculate the numerical value:
$$A_{\text{uncovered}} \approx 1017.88 \text{ m}^2$$
The area of the floor not covered by the carpet is approximately:
$$\boxed{1017.88 \text{ m}^2}$$