guided practice\nclick or tap geometry notes to see a table of cubes.\nthe volume of a sphere is…

Explanation:

Step1: Recall the volume formula of a sphere

The volume formula of a sphere is ( V = \frac{4}{3}\pi r^{3} ), where ( V ) is the volume and ( r ) is the radius of the sphere. We know that ( V=\frac{256}{3}\pi \space cm^{3} ), so we can set up the equation: [ \frac{4}{3}\pi r^{3}=\frac{256}{3}\pi ]

Step2: Solve for the radius ( r )

First, we can divide both sides of the equation by ( \frac{4}{3}\pi ) (or multiply both sides by ( \frac{3}{4\pi} )). [ r^{3}=\frac{\frac{256}{3}\pi}{\frac{4}{3}\pi}=\frac{256}{3}\pi\times\frac{3}{4\pi} = 64 ] Then, take the cube - root of both sides: ( r=\sqrt[3]{64} = 4 \space cm ).

Step3: Recall the surface area formula of a sphere

The surface area formula of a sphere is ( S = 4\pi r^{2} ), where ( S ) is the surface area and ( r ) is the radius of the sphere.

Step4: Substitute the radius into the surface area formula

We know that ( r = 4 \space cm ), substitute ( r = 4 ) into the formula ( S = 4\pi r^{2} ): [ S=4\pi\times4^{2}=4\pi\times16 = 64\pi \space cm^{2} ]

Answer:

B. ( 64\pi \space cm^{2} )