Question

Kate is the captain of a large cruise ship. As she
drives the ship, she sits 50 meters above the sea.
Paul is the captain of a boat. He sits 15 meters
above the sea. If the radius of the earth is
6,371,000 meters, how much further can Kate see
across the horizon than Paul?

Answer 1

Kate can see across the horizon by 3.33 times further than Paul.

What is the shape of the horizon?

The volume of the cone can be used to determine how far they can see across the horizon from the cone shape.

Using the volume of the cone

$\mathbf{ V=\pi r \dfrac{h }{3}}$

For Kate:

• Height (h) = 50 m
• Radius (r) = 6,371,000 m

$\mathbf{ V=\pi r \dfrac{h }{3}}$

$\mathbf{ V=\pi \times (6371000)^2 \times \dfrac{50 }{3}}$

V = 2.12526863 × 10¹⁵ m³

For Paul

• Height (h) = 15 m
• Radius (r) = 6,371,000 m

$\mathbf{ V=\pi r \dfrac{h }{3}}$

$\mathbf{ V=\pi \times (6371000)^2 \times \dfrac{15 }{3}}$

V = 6.3758059 × 10¹⁴ m³

To determine how much further can kate see across the horizon than Paul, we have:

= 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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