Dimensional analysis. Please check my working

In summary, the problem involves finding the radius of a sphere that is six times heavier than another sphere with a radius of 4.30 cm. Using the equations for volume and mass, a ratio can be set up and solved to find that the radius of the larger sphere is 9.76 cm. The mistake in the attempt at a solution was taking the cube root of the left-hand side incorrectly.
  • #1
need_aca_help
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Homework Statement


Two spheres are cut from a certain uniform rock. One has radius 4.30 cm. The mass of the other is six times greater. Find its radius.


Homework Equations


v = (4/3)(pi)(r)^3
m = vp


The Attempt at a Solution


6[(4/3)(pi)(r1)3] = (4/3)(pi)(r2)3
8(pi)(r1)3 = (4/3)(pi)(r2)3
6(r1)3 = (r2)3
6(4.3)(1/3) = 9.7568

Answer:
9.76 cm

I got this question wrong for some reason... Where is my mistake...?
 
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  • #2
need_aca_help said:


6(r1)3 = (r2)3
6(4.3)(1/3) = 9.7568

Answer:
9.76 cm

I got this question wrong for some reason... Where is my mistake...?


Going from 2nd last to last equation you made your basic mistake.
 
  • #3
I don't see it... :(
 
  • #4
If you take a sphere with radius r, and make another sphere with radius 2*r, what is the ratio of the volume of the bigger sphere to the smaller sphere?
 
  • #5
need_aca_help said:
I don't see it... :(

Take the cube root of each side. Your mistake is on the left-hand side.
Fact: (ab3)1/3 = a1/3b
 

FAQ: Dimensional analysis. Please check my working

1. What is dimensional analysis?

Dimensional analysis is a mathematical tool used in science to analyze and manipulate physical quantities by looking at their units. It involves converting units and canceling out unnecessary ones to simplify a problem and obtain a meaningful result.

2. Why is dimensional analysis important in science?

Dimensional analysis is important because it allows scientists to check the validity of equations and calculations, and also helps in predicting how a physical quantity will change under different conditions. It also helps in converting units between different systems of measurement.

3. How is dimensional analysis used in chemistry?

Dimensional analysis is commonly used in chemistry to convert units of measurement, such as mass, volume, and concentration. It is also used to check the accuracy of chemical equations and determine the relationships between different physical quantities in a chemical reaction.

4. Can dimensional analysis be used in other fields besides science?

Yes, dimensional analysis can be used in other fields such as engineering, economics, and even cooking. It is a useful tool for converting units and simplifying calculations in any situation where physical quantities are involved.

5. What are the limitations of dimensional analysis?

Dimensional analysis is a powerful tool, but it has its limitations. It cannot be used to solve problems involving non-linear relationships between physical quantities, and it cannot take into account factors such as human error or experimental uncertainty. It is also not effective for analyzing abstract concepts that do not have physical units.

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