if a globe has a diameter of 0.5 meters write the globes scale as a ratio. What distance on earth would 1 centimeter on a globe represent
To find the scale of the globe, we need to determine the ratio between the size of the globe and the corresponding distance on Earth.
First, let's calculate the circumference of the globe using its diameter. The formula for the circumference of a sphere is C = πd, where C is the circumference and d is the diameter.
Given that the diameter of the globe is 0.5 meters, we can plug this value into the formula:
C = π × 0.5
C ≈ 1.57 meters
So, the circumference of the globe is approximately 1.57 meters.
Now, let's find the scale of the globe by determining what distance on Earth is represented by 1 centimeter on the globe. To do this, we need to set up a ratio comparing the circumference of the globe to the distance on Earth.
The scale ratio can be expressed as:
1 centimeter on the globe : X distance on Earth
To find X, we can set up the following proportion:
1 centimeter / C (circumference of the globe) = X distance on Earth / total circumference of the Earth
Using the values we have:
1 cm / 1.57 m ≈ X / 40,075 km
Simplifying the proportion, we get:
(1/100) / (157/100) ≈ X / 40,075
Now, calculating X:
X ≈ (1/100) * 40,075 km / (157/100)
X ≈ 25.52 km
Therefore, 1 centimeter on the globe would represent approximately 25.52 kilometers on Earth.