length in cm of one side of perfect cube of gold with a density of 18g/cc and mass of 25g?
How would i set up this equation? I don't know what length formula I would use, because I know that i am not supposed to just divide the density by the mass, because that would be incorrect. Maybe the length would be 1/4x = Mass x Density??
mass = volume x density
25g = volume x 18 g/cc
Solve for volume in cc (cubic centimeters) = 1.389 cc.
Volume of a cube = length^3
1.389cc = length^3
So take the cube root of both sides to find
length = cube root(1.389) = 1.1157 cm which rounds to 1.1cm to two significant figures.
Thank You So Much
To find the length of one side of a perfect cube made of gold, you can use the formula for density, which is density = mass/volume. In this case, you have the mass (25g) and the density (18g/cc), so you need to rearrange the formula to solve for volume.
First, you can rearrange the density formula:
density = mass/volume
Multiply both sides by volume:
density * volume = mass
Now, divide both sides by density:
volume = mass/density
Now you have the formula for volume. Since a cube has equal side lengths, you can use this volume formula to find the length of each side.
In the case of a cube, the volume formula can be written as:
volume = length^3
Now you can substitute the formula for volume that you derived earlier:
mass/density = length^3
Plug in the given values:
25g/18g/cc = length^3
To isolate the length, cube root both sides of the equation:
(length^3)^(1/3) = (25g/18g/cc)^(1/3)
Simplify:
length = (25/18)^(1/3)
Now you can calculate the length using a calculator:
length ≈ 0.953 cm
Therefore, the length of one side of the perfect gold cube is approximately 0.953 cm.