a hollow metal sphere has an internal radius of 20cm and an external radius of 30cm , given that the density of the metal is 7.8, find the mass of the sphere , expressing your answer in kg.
just multiply the volume of metal by its density to get the mass:
cm^2 * g/cm^3 = g
You know that the volume of a sphere of radius r is
v = 4/3 πr^3
so, to get the volume of metal, just subtract the volume of the empty inner sphere from the outer sphere.
the volume of metal is
... v = 4/3 * π * (30³ - 20³) cm³
if the density units are g/cm³
then multiply v by .0078
To find the mass of the sphere, we first need to calculate the volume of the metal used.
The formula for the volume of a hollow sphere is:
V = (4/3)π(R^3 - r^3),
where V is the volume, π is the mathematical constant pi (approximately 3.14159), R is the external radius, and r is the internal radius.
So, plugging in the values:
V = (4/3)π((30^3) - (20^3))
V = (4/3)π(27000 - 8000)
V = (4/3)π(19000)
Next, we need to calculate the mass of the metal used.
The formula for calculating mass is:
M = density * V,
where M is the mass and density is the density of the metal.
So, substituting the values:
M = 7.8 * (4/3)π(19000)
Calculating this expression will give us the mass of the sphere in kg.
To find the mass of the hollow metal sphere, we need to calculate the volume of the metal and then multiply it by the density. Here's how you can do it step-by-step:
1. Calculate the volume of the metal:
The volume of a hollow sphere can be calculated by subtracting the volume of the inner sphere from the volume of the outer sphere.
The formula for the volume of a sphere is V = (4/3) * π * r^3, where "r" is the radius.
For the outer sphere:
V_outer = (4/3) * π * (30cm)^3
For the inner sphere:
V_inner = (4/3) * π * (20cm)^3
2. Subtract the volume of the inner sphere from the volume of the outer sphere:
V_metal = V_outer - V_inner
3. Calculate the mass of the metal:
Mass = Density * Volume
Given that the density of the metal is 7.8, we can now calculate the mass:
Mass = Density * V_metal (in grams)
= 7.8 * V_metal (in grams)
= 7.8 * V_metal (converted to kilograms by dividing by 1000)
Once you perform the calculations, the final answer will be the mass of the sphere expressed in kilograms.
Note: In this explanation, we assumed that the hollow metal sphere is uniformly dense and made of a single material.