Earth's diamter is about 13,000 kilometers. If a globe has a diameter of 0.5 meter, write the globes scale as a ratio. What distance on earth would 1 centimeter on the golbe represent?
To find the scale of the globe, we need to compare the diameter of the globe to the diameter of the Earth.
The diameter of the globe is given as 0.5 meters.
The diameter of the Earth is given as 13,000 kilometers.
To convert the diameter of the Earth from kilometers to meters, we multiply it by 1,000.
So, the diameter of the Earth is 13,000 kilometers x 1,000 = 13,000,000 meters.
Now we can find the scale of the globe by dividing the diameter of the globe by the diameter of the Earth.
Scale = Diameter of the globe / Diameter of the Earth
Scale = 0.5 meters / 13,000,000 meters
Simplifying the ratio, we can divide both the numerator and denominator by 0.5.
Scale = 1 meter / 26,000,000 meters
So, the scale of the globe can be written as 1:26,000,000.
To find the distance on Earth that 1 centimeter on the globe represents, we can use the same scale.
Since the scale is 1:26,000,000, we can set up a proportion:
1 centimeter on the globe = X distance on Earth
1 cm : 26,000,000 meters = X cm : Y meters
To solve for X, we can cross-multiply and divide:
X = (1 cm * Y meters) / 26,000,000 meters
The distance on Earth represented by 1 centimeter on the globe would depend on the value of Y, the chosen unit of measurement on Earth.
To find the scale of the globe, we can use the following formula:
Scale = Earth's diameter / Globe's diameter
Given that Earth's diameter is about 13,000 kilometers and the globe's diameter is 0.5 meters, we can plug in the values:
Scale = 13,000 kilometers / 0.5 meters
Now, to determine what distance on Earth 1 centimeter on the globe represents, we need to calculate it using the scale. Let's denote the distance on Earth as "x" kilometers.
Scale = Earth's distance / Globe's distance
1 centimeter on the globe represents x kilometers on Earth. Let's convert 1 centimeter to meters to match the unit of the globe's diameter:
0.01 meters on the globe represents x kilometers on Earth.
Now, we can set up the equation using the scale:
13,000 kilometers / 0.5 meters = x kilometers / 0.01 meters
Cross-multiplying, we get:
13,000 * 0.01 = 0.5 * x
130 = 0.5 * x
Dividing by 0.5, we find:
x = 130 / 0.5
x = 260
Therefore, 1 centimeter on the globe represents a distance of 260 kilometers on Earth.