Calculating the Volume of Spheres with Different Radii

[Revolver]

What is the formula? I have two problems:

1. What is the volume of a sphere with a radius of 5.0 m?

My initial guess was 5^3 = 125, but apparently the answer is 523.6.

2. The radius of the Earth is 6400 km. If the atmosphere is approximately 10 km high, then what is the volume of air around the earth?

Ok to be honest, I have no idea. I assume you find the volume of the earth, then the volume of a sphere with radius 10 km, and subtract the two... but that goes back to me not knowing the formula of volume of a sphere :D

 

[Janus]

What is the formula? I have two problems:

1. What is the volume of a sphere with a radius of 5.0 m?

My initial guess was 5^3 = 125, but apparently the answer is 523.6.
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$$v= \frac{4 \pi r^3}{3}$$

2. The radius of the Earth is 6400 km. If the atmosphere is approximately 10 km high, then what is the volume of air around the earth?

Ok to be honest, I have no idea. I assume you find the volume of the earth, then the volume of a sphere with radius 10 km, and subtract the two... but that goes back to me not knowing the formula of volume of a sphere :D

You might want to rethink that second one.

 

[E=m(C)^2]

OK, the general formula for the volume of a sphere is V=(4/3)pi(r^3), where r=radius and pi=3.14 approx.
Question 1 you just have to simply substitute r=5 into the equation. For Question 2 you find the volume of the Earth plus the atmosphere together, having a radius of 6500km, and subtract from this the volume of the Earth alone, where r=6400km. Hopefully that helps.

 

[Math Is Hard]

Here's a page with some formulas that might come in handy:
http://www.science.co.il/Formula.asp

 

[FrostScYthe]

It's two spheres but the larger one is the one that includes the atmosphere it would be (6400 + 10)Km and the smaller one would Earth's 6400 km radius to ground.