Ratio of the volume and the surface area between two spheres

by Rabbani

Question
The radius of sphere A is twice that of a sphere B. Find the ratio among their surface areas and the ratio among their volumes.

Answer
Consider the spheres below. These two spheres have the radius of 2r and r respectively.
 
Point with the coordinates (-4,0.5)
       Sphere A                           Sphere B

The ratio of  the surface area of sphere A to sphere B

Let the surface area of sphere A be SA and the surface area of sphere B be SB. Now we know that the formula for the surface area of sphere S is:  
Point with the coordinates (-4,0.5)
Therefore, to find SA, we just need to substitute r with 2r and simplify the equation. This is shown below: 
Point with the coordinates (-4,0.5)
Similarly, to find SB, since the radius is r, we have:
 
Point with the coordinates (-4,0.5)
Hence, the ratio of SA to SB will be: 

Point with the coordinates (-4,0.5)

The ratio of  the volume of sphere A to sphere B

Let the volume of sphere A be VA and the volume of sphere B be VB. Now, we know that the formula for the volume of a sphere is: 

Point with the coordinates (-4,0.5)
To find VA, we just substitute r with 2r and simplify the equation. This is shown below: 
Point with the coordinates (-4,0.5)
Next, to find VB, since the radius of sphere B is r, we have: 

Point with the coordinates (-4,0.5)

Hence, the ratio of VA to VB is: 
Point with the coordinates (-4,0.5)



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Mar 21, 2011
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thank you :)
by: Alannis

this has helped me an awful lot for my homework :) so thank you to whoever made this page!!

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