Answer:
radius = 2.05 units
Step-by-step explanation:
The volume of a sphere is given by the formula: [tex]V=\frac{4}{3} \pi r^3[/tex]. In this formula:
- V = volume of the sphere
- r = radius of the sphere
Since we are given the volume of the sphere (36 units^3), we just need to solve for r in the equation for the volume of a sphere.
Substitute 36 for V into the formula and solve for r.
[tex]36=\frac{4}{3} \pi r^3[/tex]
Divide both sides by [tex]\frac{4}{3}[/tex]. To do this, multiply 36 by the reciprocal of [tex]\frac{4}{3}[/tex].
- [tex]36\times \frac{3}{4}[/tex]
- [tex]36\times \frac{3}{4} =\frac{108}{4} \rightarrow 27[/tex]
Simplify and rewrite the equation.
[tex]27=\pi r^3[/tex]
Now divide both sides of the equation by pi ([tex]\pi[/tex]).
- [tex]27\div\pi=8.59436692696[/tex]
Rewrite the equation.
[tex]8.59436692696=r^3[/tex]
To isolate and solve for r, cube root both sides of the equation.
- [tex]r=\sqrt[3]{8.59436692696}[/tex]
- [tex]r=2.04835218977[/tex]
The radius of this sphere is 2.04835218977 units. If your question wants this rounded to the nearest:
- whole number: 2 units
- tenth: 2.0 units
- hundredth: 2.05 units
- thousandth: 2.048 units
I'll just give the answer rounded to the nearest hundredth as that seems the most popular.
