How to Calculate the Mass of a Material for a Hollow Spherical Shell?

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To calculate the mass of a hollow spherical shell with inner radius r1 and outer radius r2, the volume of the shell must first be determined. The volume of the hollow sphere can be expressed as the difference between the volumes of two spheres: V = (4/3)π(r2^3 - r1^3). The mass can then be calculated using the formula mass = density (p) multiplied by volume, resulting in mass = p * (4/3)π(r2^3 - r1^3). This approach allows for expressing the mass in terms of p, r1, and r2 without needing specific numerical values. Understanding the distinction between the volume of a sphere and a spherical shell is crucial for accurate calculations.
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What mass of a material with density p is required to make a hollow spherical shell having inner radius r1 and outer radius r2?

How do I get the volume of the hollow sphere without any numbers?

Any help would be greatly appreciated!
 
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chanv1 said:
What mass of a material with density p is required to make a hollow spherical shell having inner radius r1 and outer radius r2?

How do I get the volume of the hollow sphere without any numbers?

Any help would be greatly appreciated!


Give your answer in terms of p, r1 and r2. To start, find the volume of the hollow sphere in terms of r1
 
I know the volume of a hollow sphere is V = 4/3 pi r^3. But how do I get the answer in terms of p, r1, and r2 without having any given numbers?
 
chanv1 said:
I know the volume of a hollow sphere is V = 4/3 pi r^3. But how do I get the answer in terms of p, r1, and r2 without having any given numbers?

V = 4/3 pi r^3 is the volume of a sphere, hollow or not.

Give your answer in terms of p, r1, and r2, not in terms of any given numbers (which are not given).

Equivalently, you may treat p, r1 and r2 as your "given numbers".
 
Your answer won't be an integer, but will contain "r1, and r2." Where you would normally put the numerical value of these unknowns, you leave them as "r1," and "r2."

It also might be more helpful to think of "volume of the hollow sphere," as the "volume of the spherical shell." The volume of a sphere is 4/3πr3, while the volume of a spherical shell is...
 
Thanks for the help!
 
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