If the volume of a sphere is 36 cubic units, what is the radius? 3 units 4√3 units 9 units

Accepted Solution

Answer:radius = 2.05 unitsStep-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 spherer = radius of the sphereSince 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 unitstenth: 2.0 unitshundredth: 2.05 unitsthousandth: 2.048 unitsI'll just give the answer rounded to the nearest hundredth as that seems the most popular.