There are 4 main characteristics that the new planet must have: 1.The outer surface must be mostly water. 2.It can't have any predators that are too dangerous for the Kelptons to deal with. 3.It must be just the right distance from its star because that determines the planet's temperature. If it's too hot or too cold, the Kelptons can't live there. They prefer temperatures between 30 and 35 degrees Celsius. 4.There must be at least 3,000,000,000,000 kiloliters of habitable water for all their people to live comfortably.
Obi-Wan has found a planet that appears to be mostly water on the surface. However, to be sure, he's going to send a probe droid down to the planet to determine its surface temperature and to find out what's under the surface of the water.
The probe droid starts sending back information starting with the surface temperature. The temperature is reported to be 88 degrees Fahrenheit. Apparently someone didn't tell the droid they needed the temperature in Celsius! Oh well, Obi-Wan can easily convert the temperature with this formula: What's the temperature in Celsius? (Round to nearest hundredth) Is that good for the Kelptons? °C
Now the probe droid is going into the water. After descending 40 km, it reports no signs of dangerous predators. However, it also reports that it's beginning to malfunction due to the extreme pressure under that much water. It's repulsors, which let it move, have been crushed, so it continues to sink into the depths and can't come back up. At 60 km, the probe droid sends it's final report before the water pressure crushes the rest of it. It reports that there are two more layers under the surface layer of water.
Because of the extreme pressure hundreds of kilometers under the water, a layer of exotic ice has formed. It's not as cold as normal ice. However, that's another lesson in a different subject. The next and final layer is actually the center of the planet. It's just a ball of rock.
Water Layer 1000 km deep Solid Rock Planet Core 100 km radius Exotic Ice Layer 3000 km deep Final Droid Data Burst Incoming…
Obi-Wan is going to use these measurements to determine if there's enough water on the planet for the Kelptons. He doesn't need to worry about the outer atmosphere because the Kelptons will obviously live below that. First he needs to know the formula for the volume of a sphere. He knows he can't determine the volume just by using the water layer alone. He needs to know the radius of the entire planet first. To find this, he adds the depths of the layers. What is the radius of the planet? km
Now he needs to know the radius of the inner two layers. To find this, he adds the depths of the inner two layers. What is the radius of the inner two layers? Obi-Wan now has to find the volume of the planet. He uses the radius of the entire planet for this. What is the volume of the entire planet? (Round to the nearest whole number) km km³
Next, he needs to find out the volume of the inner two layers. Even without the water layer, the inner two layers are still a sphere, so he works the formula with the radius of the inner two layers. What is the volume of the inner two layers? (Round to the nearest whole number) Now that Obi-Wan knows the volume of the inner two layers and the entire planet, he can determine the volume of the water layer by simply subtracting the inner volume from the planet volume. What is the volume of the water layer? (Round to the nearest whole number) km km³
Now he knows the volume in cubic kilometers, but we need to convert it to kiloliters. Remember, one liter equals one cubic decimeter. Since Obi- Wan knows this, he first converts the cubic kilometers to cubic decimeters. What is the water volume in cubic decimeters? What is the water volume in cubic decimeters? Now, he converts the cubic decimeters to liters. Since they are the same, this is simple. What is the water volume in liters? What is the water volume in liters? Obi-Wan needs to know the volume in kiloliters, so he converts the volume in liters to kiloliters. What is the water volume in kiloliters? What is the water volume in kiloliters? dm³ L kL
The Kelptons need 3,000,000,000,000 kiloliters of water on their new home planet. Does this planet meet that requirement? All requirements are met by this planet! The Kelptons can begin colonizing New Kelpto! Just for fun, let's determine the volume of the solid rock planet core. What is the volume of the planet core? (Round to the nearest whole number) km³