Question

How many times can a three-dimensional object that has a radius of 1,000 units fit something with a radius of 10 units inside of it? How many times can something with a radius of 2,000 units fit something with a radius of 1 unit?

Answer 1

# _units = 1000

Step-by-step explanation:

This exercise we can use a direct proportion rule.

If a volume of radius r = 1 is one unit, how many units can fit in a volume of radius 10?

# _units = V₁₀ / V₁

The volume of a body of radius 1 is

V₁ = 4/3 π r₁³

V₁ = 4/3π

the volume of a body of radius r = 10

V₁₀ = 4/3 π r₂³

V10 = 4/3 π 10³

the number of times this content is

#_units = 4/3 π 1000 / (4/3 π 1)

# _units = 1000