- The circumference of a circle is calculated as \(c = \pi d\).
- For a pot with \(c = 40.82 \text{ cm}\), the diameter is \(13 \text{ cm}\) and the radius is \(6.5 \text{ cm}\).
- A circular stage with \(d = 32 \text{ ft}\) has an area of \(803.84 \text{ sq ft}\).
- A pool design consisting of three semicircles of \(10 \text{ ft}\) diameter has a perimeter of approximately \(14.4 \text{ m}\).
- Final answers: \(c = \pi d \text{ (Part 1)}\); \(d=13\text{ cm}, r=6.5\text{ cm} \text{ (Part 2)}\); \(A=803.84\text{ sq ft} \text{ (Part 3)}\); \(P \approx 14.4\text{ m} \text{ (Part 4)}\).
Explanation
- Step-by-step calculations for circular dimensions.
- For the first circle, the circumference is calculated using the formula \(c = \pi \cdot d\). Without a provided image, we express the circumference in terms of the diameter \(d\): \(c = \pi d\).
- For the cooking pot, given the circumference \(c = 40.82 \text{ cm}\) and \(\pi \approx 3.14\), the diameter \(d\) is calculated as \(d = \frac{c}{\pi} = \frac{40.82}{3.14} = 13 \text{ cm}\). The radius \(r\) is half of the diameter, so \(r = \frac{13}{2} = 6.5 \text{ cm}\).
- For the circular stage with diameter \(d = 32 \text{ feet}\), the radius is \(r = \frac{32}{2} = 16 \text{ feet}\). Using \(\pi \approx 3.14\), the area \(A\) is \(A = \pi \cdot r^2 = 3.14 \cdot (16)^2 = 3.14 \cdot 256 = 803.84 \text{ square feet}\).
- For the swimming pool design consisting of three semicircles with diameter \(d = 10 \text{ feet}\), the total distance around is calculated based on the combined arcs. Using the arc length of a semicircle \(\frac{1}{2} \cdot \pi \cdot d\), the distance is \(3 \cdot (\frac{1}{2} \cdot 3.14 \cdot 10) = 47.1 \text{ feet}\). Converting this to meters using \(1 \text{ foot} \approx 0.3048 \text{ meters}\), we get \(47.1 \cdot 0.3048 = 14.35608 \text{ meters}\). Rounded to the nearest tenth, this is \(14.4 \text{ meters}\).
Examples
Geometry is essential in everyday life. For instance, knowing how to calculate the area and circumference helps in home improvement projects, like buying the right size circular rug for your living room or determining the amount of tiles needed for a circular fountain, ensuring your designs are both precise and efficient.