Answer:
d = {∛ [tex]\frac{V}{(4/3)(pi)}[/tex]} x (2) (see below for explanation)
If volume = 34, d ≈ 4
Step-by-step explanation:
The volume of a sphere is:
V = (4/3) · π · r³
To find the diameter, you need to find the radius first. Isolate it to one side:
[tex]\frac{V}{(4/3)(pi)}[/tex] = r³
r³ = [tex]\frac{V}{(4/3)(pi)}[/tex]
∛r³ = ∛ [tex]\frac{V}{(4/3)(pi)}[/tex]
r = ∛ [tex]\frac{V}{(4/3)(pi)}[/tex]
So you would first multiply 4/3 by pi, then divide volume by that. Then cube root the whole thing. This will get you the radius.
Double this. This will get you the diameter.
r = ∛ [tex]\frac{V}{(4/3)(pi)}[/tex]
d = {∛ [tex]\frac{V}{(4/3)(pi)}[/tex]} x (2)
If the volume is 34, then:
d = {∛ [tex]\frac{34}{(4/3)(pi)}[/tex]} x (2)
4/3 (pi) = 4.188...
34/41.88... = 8.116...
∛8.116... = 2.009...
2.009...(2) = 4.019...
d = 4.019389542
d ≈ 4
