Question

If the volume of a sphere is 256π/3 what is the radius?

Answer 1

Answer:

$\boxed {\boxed {\sf r=4}}$

Step-by-step explanation:

The volume of a sphere is calculated using the following formula:

$v= \frac{4}{3} \pi r^3$

The volume of the sphere is $\frac {256 \pi}{3}$. Substitute this value in for v.

$\frac{256 \pi}{3} = \frac{4}{3} \pi r^3$

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

$\frac {3}{4 \pi} *\frac{256 \pi}{3} = \frac{4}{3} \pi r^3 *\frac {3}{4 \pi}$

$\frac {3}{4 \pi} *\frac{256 \pi}{3} = r^3$

$64 =r^3$

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.

$\sqrt[3]{64}=\sqrt[3]{r^3}$

$\sqrt[3]{64}=r$

$4=r$

The radius of the sphere is 4.

Answer 2

Answer:

4

Step-by-step explanation:

The volume of a sphere is equal to 4/3πr³.

Set up the equation;

4/3πr³=256π/3

Multiple both sides by 3/(4π):

r³=64

r=∛64=4 (ans)