What is the ratio V2/V1 of the volumes?

In summary, the ratio V2/V1 represents the relationship between two volumes, and is calculated by dividing the value of V2 by the value of V1. It can be greater or less than 1, indicating the size difference between the two volumes. In science, it is used to compare substances, calculate concentrations, and analyze changes in volume or capacity.
  • #1
tenchick19
6
0
I need help with this question: Sphere 1 has surface area A1 and volume V1, and Sphere 2 has surface area A2 and volume V2. If the radius of Sphere 2 is six times the radius of Sphere 1, what is the ration A2/A1 of the areas?

Part two: What is the ratio V2/V1 of the volumes?

:confused:
 
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  • #2
For a sphere with radius R, area (A) and volume (V) are:

[tex]\begin{array}{l}
A = 4\pi R^2 \\
V = \frac{4}{3}\pi R^3 \\
\end{array}[/tex]

With your knowledge of the ratio's of the radii, that should help :smile:
 
  • #3


I can provide a mathematical explanation for the ratio of volumes V2/V1. The volume of a sphere is calculated using the formula V = (4/3)πr^3, where r is the radius of the sphere. Therefore, the ratio of volumes V2/V1 can be calculated as (4/3)πr2^3 / (4/3)πr1^3, where r2 is the radius of Sphere 2 and r1 is the radius of Sphere 1.

Substituting the given information that the radius of Sphere 2 is six times the radius of Sphere 1, we get (4/3)π(6r1)^3 / (4/3)πr1^3. Simplifying this expression, we get (6^3) / 1, which is equal to 216. Therefore, the ratio of volumes V2/V1 is 216:1.

For the second part of the question, the ratio of areas A2/A1 can be calculated using the formula A = 4πr^2, where r is the radius of the sphere. Substituting the given information, we get A2/A1 = (4π(6r1)^2) / (4πr1^2), which simplifies to 36:1. Thus, the ratio of areas A2/A1 is 36:1.

In summary, the ratio of volumes V2/V1 is 216:1 and the ratio of areas A2/A1 is 36:1.
 

1. What does the ratio V2/V1 represent?

The ratio V2/V1 represents the relationship between two volumes, V2 and V1. It is a mathematical expression that shows how many times one volume is greater or smaller than the other.

2. How do you calculate the ratio V2/V1?

To calculate the ratio V2/V1, you simply divide the value of V2 by the value of V1. For example, if V2 is 10 and V1 is 5, the ratio V2/V1 would be 10/5 = 2.

3. Can the ratio V2/V1 be greater than 1?

Yes, the ratio V2/V1 can be greater than 1. This means that V2 is larger than V1 and the ratio is expressing how many times larger it is.

4. What does it mean if the ratio V2/V1 is less than 1?

If the ratio V2/V1 is less than 1, it means that V2 is smaller than V1 and the ratio is expressing how many times smaller it is. For example, if V2 is 2 and V1 is 5, the ratio V2/V1 would be 2/5 = 0.4.

5. How is the ratio V2/V1 used in science?

The ratio V2/V1 is used in science to compare two volumes of substances or solutions. It can also be used to calculate concentrations, dilutions, and other measurements. In addition, it is commonly used in physics and engineering to analyze changes in volume or capacity.

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