Answer:
[tex]\boxed {\boxed {\sf r=4}}[/tex]
Step-by-step explanation:
The volume of a sphere is calculated using the following formula:
[tex]v= \frac{4}{3} \pi r^3[/tex]
The volume of the sphere is [tex]\frac {256 \pi}{3}[/tex]. Substitute this value in for v.
[tex]\frac{256 \pi}{3} = \frac{4}{3} \pi r^3[/tex]
We are solving for the radius, so we must isolate the variable r. It is being multiplied by 4/3π. We can divide by this fraction or multiply by the reciprocal. The reciprocal is the fraction flipped, or 3/4π
[tex]\frac {3}{4 \pi} *\frac{256 \pi}{3} = \frac{4}{3} \pi r^3 *\frac {3}{4 \pi}[/tex]
[tex]\frac {3}{4 \pi} *\frac{256 \pi}{3} = r^3[/tex]
[tex]64 =r^3[/tex]
The variable is being cubed. The inverse of a cube is the cube root, so we take the cube root of both sides of the equation.
[tex]\sqrt[3]{64}=\sqrt[3]{r^3}[/tex]
[tex]\sqrt[3]{64}=r[/tex]
[tex]4=r[/tex]
The radius of the sphere is 4.
