Let's calculate the areas of the sails first:
Sails
Sail A:
- Base: 6 m
- Height: Let's choose 7 m (within the given range of 5 to 8 m).
- Area = (Base * Height) / 2 = (6 * 7) / 2 = 21 m²
Sail B:
- To be moderately larger than Sail A, we can choose a base of 8 m and a height of 7 m.
- Area = (Base * Height) / 2 = (8 * 7) / 2 = 28 m²
Sail C:
- Sail C has an area less than twice the area of Sail A, so its maximum area can be calculated as less than 42 m² (2 * 21).
- Let's choose an area of 35 m² for Sail C.
- We assume a base of 10 m, so:
- Area = 35 m² ⇒ 35 = (Base * Height) / 2 ⇒ Base * Height = 70
- If we choose a base of 10 m, then Height = 70 / 10 = 7 m.
Now we can fill in the table for the sails:
| Dimension | Sail A | Sail B | Sail C | |----------------|---------|---------|---------| | Base length | 6 m | 8 m | 10 m | | Height | 7 m | 7 m | 7 m | | Area | 21 m² | 28 m² | 35 m² |
Portholes
Porthole A:
- The circumference is between \(2\pi\) and \(6\pi\). Let's select \(4\pi\).
- To find the radius: Circumference = \(2\pi r\) ⇒ \(r = \frac{Circumference}{2\pi} = \frac{4\pi}{2\pi} = 2\) feet.
- Area = \(\pi r^2 = \pi (2^2) = 4\pi\) square feet.
Porthole B:
- Let's select \(5\pi\) for its circumference.
- Radius = \(r = \frac{5\pi}{2\pi} = 2.5\) feet.
- Area = \(\pi (2.5^2) = 6.25\pi\) square feet.
Porthole C:
- Given that its circumference is less than three times that of Porthole A, we can select \(8\pi\).
- Radius = \(r = \frac{8\pi}{2\pi} = 4\) feet.
- Area = \(\pi (4^2) = 16\pi\) square feet.
Now we can fill in the table for the portholes:
| Dimension | Porthole A | Porthole B | Porthole C | |----------------|------------|------------|------------| | Radius | 2 ft | 2.5 ft | 4 ft | | Circumference | \(4\pi\) | \(5\pi\) | \(8\pi\) | | Area | \(4\pi\) | \(6.25\pi\)| \(16\pi\) |
These tables summarize the possible areas and dimensions for the sails and portholes based on the constraints provided.