Kate can see across the horizon by 3.33 times further than Paul.
What is the shape of the horizon?
The assumed shape of the horizon shows that it forms a cone shape. The volume of the cone can be used to determine how far they can see.
The volume of the cone [tex]\mathbf{ V=\pi r \dfrac{h }{3}}[/tex]
For Kate:
- Height (h) = 50 m
- Radius (r) = 6,371,000 m
[tex]\mathbf{ V=\pi r \dfrac{h }{3}}[/tex]
[tex]\mathbf{ V=\pi \times (6371000)^2 \times \dfrac{50 }{3}}[/tex]
V = 2.12526863 × 10¹⁵ m³
For Paul
- Height (h) = 15 m
- Radius (r) = 6,371,000 m
[tex]\mathbf{ V=\pi r \dfrac{h }{3}}[/tex]
[tex]\mathbf{ V=\pi \times (6371000)^2 \times \dfrac{15 }{3}}[/tex]
V = 6.3758059 × 10¹⁴ m³
To determine how much further can kate see across the horizon than Paul, we have:
= Volume of Kate/Volume of Paul
= 2.12526863 × 10¹⁵ m³/6.3758059 × 10¹⁴ m³
= 3.33 times further.
Learn more about Plane shapes here:
https://brainly.com/question/4504103
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