So, I need to find the mass of a cube. I have diameter of 16.4 micrometers, and density of 1,000 kg/m3. I can find all kinds of formulas for spheres, but not for cubes?
for a cube of side s, the volume is s^3
that's why the third power is called "cubed"!
But, since when do cubes have diameters?
THis is the question posed to me by mi bio teacher. THe more specific of it it is, "find the masss of a liver cell, assuming it has the shape of a cube, with the diameter and density of water."
To find the mass of a cube, you need to know the edge length (or side length) of the cube, rather than the diameter. The diameter is a measurement typically used for spheres and circles.
To find the edge length of a cube, you can use the diameter (D), as you have provided. Since the diameter is the distance across the cube passing through its center, if you divide the diameter by √3, you will get the edge length (L).
L = D / √3
In this case, you have a diameter of 16.4 micrometers. Converting micrometers to meters by dividing by 1,000,000, you get:
D = 16.4 × 10^(-6) meters.
Now, you can calculate the edge length (L):
L = (16.4 × 10^(-6)) / √3
Once you have calculated the edge length of the cube, you can use the density (ρ) to find the mass (m) using the formula:
m = ρ * V
where V represents the volume of the cube.
The volume of a cube is given by:
V = L^3
Now that you have determined the edge length (L), you can simply substitute it into the volume formula to find the volume of the cube.
Finally, multiply the volume by the density to calculate the mass of the cube.