Calculating Copper Volume for Hollow Spherical Shell

The volume of a sphere is (4/3)*pi*r^3In summary, to make a hollow spherical shell with inner radius of 5.70 cm and outer radius of 5.75 cm, the density of copper is 8.92 g/cm^3. The volume of the shell can be found using the equation (4/3)*pi*r^3, where r is the radius given. To find the height, we do not need it as the sphere is symmetric and the radius gives the distance from center to edge in any direction.
  • #1
babysnatcher
91
0
How many grams of copper are required to make a hollow spherical shell having an inner radius of 5.70 cm and an outer radius of 5.75 cm? The density of copper is 8.92 g/cm^3.

Ok, so, how do I find the height? Or solve the problem without the height?
 
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  • #2
It's a hollow sphere, and you are given the inner and outer radii.

What height are you talking about?
 
  • #3
babysnatcher said:
How many grams of copper are required to make a hollow spherical shell having an inner radius of 5.70 cm and an outer radius of 5.75 cm? The density of copper is 8.92 g/cm^3.

Ok, so, how do I find the height? Or solve the problem without the height?

Height?

It's a sphere. It's symmetric. If you are given a radius, that gives you the distance from centre to edge in ANY direction.

Do you know the equation for the volume of a sphere? (I edited this post)
 
Last edited:
  • #4
Oh, my bad xD! When I saw shell, I immediately thought cylinder.
 
  • #5


To solve this problem, you do not need to find the height. The volume of a hollow spherical shell can be calculated using the formula V = (4/3)π(R^3 - r^3), where R is the outer radius and r is the inner radius. In this case, R = 5.75 cm and r = 5.70 cm. Plugging these values into the formula, we get V = (4/3)π(5.75^3 - 5.70^3) = 19.6 cm^3.

Since the density of copper is 8.92 g/cm^3, we can use the formula density = mass/volume to find the mass of copper needed. Rearranging the formula, we get mass = density x volume. Plugging in the values, we get mass = 8.92 g/cm^3 x 19.6 cm^3 = 175.23 g.

Therefore, approximately 175.23 grams of copper are required to make a hollow spherical shell with an inner radius of 5.70 cm and an outer radius of 5.75 cm.
 

1. How do you calculate the volume of a hollow spherical shell made of copper?

To calculate the volume of a hollow spherical shell made of copper, you can use the formula V = (4/3)πr3 - (4/3)πr13, where r is the outer radius and r1 is the inner radius.

2. What are the units for the volume of a hollow spherical shell?

The units for the volume of a hollow spherical shell are cubic units, such as cubic centimeters (cm3) or cubic meters (m3).

3. Can the same formula be used for calculating the volume of a solid copper sphere?

No, the formula for calculating the volume of a solid sphere is V = (4/3)πr3, which does not account for the inner radius of a hollow spherical shell.

4. How can the volume of a hollow spherical shell be used in real-world applications?

The volume of a hollow spherical shell can be used to determine the amount of copper needed to create a specific size and thickness of a copper container, such as a copper bowl or vase.

5. Are there any limitations to using this formula for calculating the volume of a hollow spherical shell?

Yes, this formula assumes that the thickness of the shell is uniform and that the inner and outer radii are measured from the center of the sphere. It may not be accurate for irregularly shaped hollow spherical shells.

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