A sphere has a radius of 5 m. How many 5cm diameter spheres can it contain?

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In summary, volume refers to the amount of space occupied by an object or substance, while conversions refer to the process of changing between units of measurement. To convert between different units of volume, conversion factors can be used. The formula for calculating volume varies depending on the shape of the object. Temperature can affect the volume of a substance due to thermal expansion or contraction. The relationship between volume and density is that as volume decreases, density increases and vice versa.
  • #1
Power of One
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Homework Statement


A sphere has a radius of 5 m. How many 5cm diameter spheres can it contain?


Homework Equations


Volume of a sphere= 4/3π r^3


The Attempt at a Solution


5m=500 cm

volume of large sphere/ volume of small sphere
4/3π (500)^3/ 4/3π (2.5)^3

=8,000,000 spheres

This answer doesn't seem reasonable. What am I doing wrong?
 
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  • #3



Hi Andreas,

Your attempt at a solution is correct, but there is a slight error in the calculation. The volume of a larger sphere should be divided by the volume of a smaller sphere, not multiplied. So the correct calculation would be:

Volume of large sphere/ volume of small sphere
(4/3π(500)^3)/(4/3π(2.5)^3)

= (4/3π(125000000)/(4/3π(15.625))

= 100000000/15.625

= 6400000

Therefore, the number of 5 cm diameter spheres that can fit in a sphere with a radius of 5 m is 6,400,000, which seems like a more reasonable answer. I hope this helps! Let me know if you have any other questions.
 

1. What is the difference between volume and conversions?

Volume refers to the amount of space occupied by an object or substance, while conversions refer to the process of changing from one unit of measurement to another.

2. How do I convert between different units of volume?

To convert between different units of volume, you can use conversion factors. For example, to convert from liters to milliliters, you would multiply the number of liters by 1000. It is important to keep track of the units and make sure they cancel out to get the desired result.

3. What is the formula for calculating volume?

The formula for calculating volume depends on the shape of the object. For regularly shaped objects, such as cubes or cylinders, the formula is simply length x width x height. For irregularly shaped objects, the volume can be calculated by measuring the displacement of water when the object is submerged.

4. How does temperature affect volume?

Temperature can affect the volume of a substance due to thermal expansion or contraction. As temperature increases, most substances expand and therefore have a larger volume. This is important to keep in mind when working with precise measurements and when converting between units.

5. What is the relationship between volume and density?

Density is a measure of how much mass is contained in a given volume. The more tightly packed the molecules are, the higher the density will be. Therefore, as the volume of a substance decreases, the density increases and vice versa.

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