Earth has a radius of about 12,500 km. If the volume of the earth were to remain the same, but the shape of the earth was a cube, what would be the approximate length of one side of the cube?
A.)12,500 km B.)15,240 km
C.)20,150 km
volume of earth =(4/3)π (12500)^3 = appr.8.18123*10^12 km^3 (I stored answer in my calculator's memory)
x^3 = 1.18123 * 10^12
x = cube root(1.18123*10^3)= 20150 km
To find the approximate length of one side of the cube with the same volume as the Earth, we need to first calculate the volume of a sphere with a radius of 12,500 km.
The volume of a sphere is given by the formula: V = (4/3) * π * r^3
Substituting the radius of the Earth, we have: V = (4/3) * π * (12,500 km)^3
Next, we need to find the length of one side of the cube with the same volume. Since the volume of a cube is given by the formula: V_cube = side^3
We can equate the volume of the sphere to the volume of the cube and solve for the length of one side of the cube.
(4/3) * π * (12,500 km)^3 = side^3
Now, let's calculate the length of one side of the cube:
(4/3) * π * (12,500 km)^3 = side^3
Divide both sides by (4/3) * π:
(12,500 km)^3 = side^3
Take the cube root of both sides to solve for the side length:
side = ∛((12,500 km)^3)
Using a calculator, we find that the approximate length of one side of the cube is:
side ≈ 15,240 km
Therefore, the correct answer is B.) 15,240 km.