A student creates a scale model of planets where 1 centimeter (cm) is equal to 10,000 kilometers (km). In this model, which planet would have a diameter of approximately 12 cm?(1 point)
Responses
Earth
Earth
Jupiter
Jupiter
Mars
Mars
Saturn
Saturn
Jupiter
A student creates a scale model of planets where 1 centimeter (cm) is equal to 10,000 kilometers (km). In this model, which planet would have a diameter of approximately 12 cm?(1 point)
Responses
Earth
Earth
Jupiter
Jupiter
Mars
Mars
Saturn
Saturn
Mars
To find out which planet in the scale model would have a diameter of approximately 12 cm, we can use the given scale where 1 cm represents 10,000 km.
Let's calculate the actual diameter of the planet represented by 12 cm in the scale model:
Actual Diameter = Scale Factor x Model Diameter
Given that the scale factor is 10,000 km/cm and the model diameter is 12 cm, we can calculate the actual diameter:
Actual Diameter = 10,000 km/cm x 12 cm
Actual Diameter = 120,000 km
This means that in the scale model, the planet with a diameter of approximately 12 cm would represent a planet with an actual diameter of 120,000 km.
Now, we need to determine which planet has a diameter closest to 120,000 km. Let's check the options:
1. Earth: Earth's actual diameter is approximately 12,742 km, which is not close to 120,000 km.
2. Jupiter: Jupiter's actual diameter is approximately 139,820 km, which is not close to 120,000 km.
3. Mars: Mars's actual diameter is approximately 6,779 km, which is not close to 120,000 km.
4. Saturn: Saturn's actual diameter is approximately 116,460 km, which is close to 120,000 km.
Based on the calculations, the planet in the scale model with a diameter of approximately 12 cm would represent Saturn.
To determine which planet would have a diameter of approximately 12 cm in this scale model, we need to find the actual diameter of each planet and then calculate its scaled value.
First, let's find the actual diameter of each planet:
- Earth: The actual diameter of Earth is approximately 12,742 kilometers.
- Jupiter: The actual diameter of Jupiter is approximately 143,000 kilometers.
- Mars: The actual diameter of Mars is approximately 6,779 kilometers.
- Saturn: The actual diameter of Saturn is approximately 120,536 kilometers.
Next, we will calculate the scaled value for each planet using the given scale of 1 cm = 10,000 km:
- Earth: Scaled value = (12,742 km) / (10,000 km/cm) = 1.2742 cm
- Jupiter: Scaled value = (143,000 km) / (10,000 km/cm) = 14.3 cm
- Mars: Scaled value = (6,779 km) / (10,000 km/cm) = 0.6779 cm
- Saturn: Scaled value = (120,536 km) / (10,000 km/cm) = 12.0536 cm
Based on these calculations, we can see that the planet with a diameter of approximately 12 cm in this scale model is Saturn.