Question

The Milky Way has a radius of approximately 50,000 light years. The visible universe has a size of approximately 15 billion light years. If the Milky Way is represented by an 8 centimeter wide coffee cup , how big would the rest of the universe be in kilometers?

Answer 1

Answer: 12 km

Explanation:

The width of the coffee cup is 8 cm. This is the diameter of the coffee cup. You need to calculate the radius of the coffee cup with this formula:

`r=(d)/(2)`

Where "d" is the diameter.

Sybstitutiing, you get:

`r=(8cm)/(2)\\\\r=4cm`

Therefore, now you know that 4 cm represents the radius of Milky Way (approximately 50,000 light years), then the rest of the universe in centimeters is represented with:

`x=((15,000,000,000\ light\ years)(4cm))/((50,000\ light\ years))=1,200,000cm`

From cm to km:

`x=(1,200,000cm)((1km)/(100,000cm))=12km`

Answer 2

24 kilometers

Explanation:

It's a simple calculation using cross multiplication:

We have the following ratios:

`(8)/(x) = (50,000)/(15,000,000,000) \\\\x * 50,000 = 8 * 15,000,000,000\\\\x = 2,400,000`

That's 2.4 million of cm... or 24 000 meters... or 24 kilometers.

That's equivalent to 300,000 cups placed side by side. That's a long way!