# Finding Radius of Aluminum Sphere

• chocolatelover
In summary, to balance an iron sphere on an equal-arm balance using an aluminium sphere, the aluminium sphere must be the same mass as the iron sphere.
chocolatelover
[SOLVED] sphere problem

## Homework Statement

One cubic meter of aluminum has a mass of 2.70 x 10^3 kg, and the same volume of iron has a mass of 7.86X 10^3 kg. Find the radius of a solid aluminum sphere that will balance a solid iron sphere of radius 1.80 cm on an equal-arm balance.

## Homework Equations

volume of a sphere=4/3pir^3

## The Attempt at a Solution

I would first need to convert everything into cm and then set 4/3pir^3=4/3pi1.80^3 and solve for r, right? I don't need to do anything with the mass, right?

You can work out the densities of each substance. Once you do this you can work out how much mass is in the iron sphere and the volume of an aluminium sphere that would be equal.

Thank you very much

I know that the formula for finding density is m/v

So, I got 2.70X10^3kg/m^3 and 7.86X10^3kg/m^3 Is that correct so far?

I don't understand the second part.

Woud I set 7.86X10^3= something

Don't I need the 1.80 cm for something?

Thank you

Last edited:
Yes, you need to work out the volume of the iron sphere to work out what its mass is.

Well, I know that the formula for finding the volume of a sphere is 4/3pir^3 and the volume of both is 1.00 m^3 (as givin) so wouldn't I just solve for r?

4/3pir^3=4/3pi1.80
r=1.342

Thank you

The masses of those meter cubed volumes are only given so you can work out the density. A sphere of radius 1.8 cm doesn't have a volume of 1 meter cubed.

If you do it algebraically obviously you won't have to work out the volume and then the mass, you can just manipulate the variables and plug the numbers in at the end.

Last edited:
Thank you very much

If you do it algebraically obviously you won't have to work out the volume and then the mass, you can just manipulate the variables and plug the numbers in at the end.

Could you please show me what you mean? How would you do it algebraically?

Thank you

You know the aluminium sphere must be the same mass as the iron sphere to balance. Therefore:

$$\rho_{al}\frac{4}{3} \pi r_1^3 = \rho_{fe}\frac{4}{3} \pi r_2^3$$

then one would solve for $r_1$.

Thank you very much

What is the pal and pfe? Don't I need to know what r2 is in order to solve for r1?

Thank you

$\rho_{al}$ and $\rho_{fe}$ are the densities of the aluminium and the iron respectively. r2 is just 1.8 cm for the iron sphere.

Do I need to do dimensional analysis or would 1.8 be the final answer?

Thank you

chocolatelover said:
Do I need to do dimensional analysis?

No. I think you're trying to make this a lot harder than it is. you have all the variables but the one you want to find. All you have to do is rearrange the equation and put the numbers in.

So, I just need to solve for r?

2.70X10^3kg(4/3pi)r^3=7.86(4/3)1.8^3

r=2.57016
r=2.57

Looks good to me. Its a lot easier if you rearrange the symbols then put the numbers in.

Thank you very much

Regards

## 1. What is the formula for finding the radius of an aluminum sphere?

The formula for finding the radius of an aluminum sphere is r = (3V/4π)^1/3, where V is the volume of the sphere.

## 2. How do I measure the volume of an aluminum sphere?

The volume of an aluminum sphere can be measured by using the formula V = (4/3)πr^3, where r is the radius of the sphere. Alternatively, you can measure the diameter and use the formula V = (π/6)D^3, where D is the diameter.

## 3. Can I use a ruler to measure the radius of an aluminum sphere?

No, a ruler is not a precise enough tool to measure the radius of an aluminum sphere. It is recommended to use a caliper or a measuring tape for more accurate results.

## 4. What is the standard unit of measurement for the radius of an aluminum sphere?

The standard unit of measurement for the radius of an aluminum sphere is meters (m). However, it can also be measured in centimeters (cm) or millimeters (mm) depending on the size of the sphere.

## 5. Can I use the same formula for finding the radius of any type of sphere?

Yes, the formula for finding the radius of an aluminum sphere can also be used for other types of spheres, such as iron or plastic. However, the density of the material will affect the value of the volume and therefore, the radius.

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