Question

Find the diameter of the sphere. The volume is 256/3 pi yd^3

Answer 1

$$\bf
\text{volume of a sphere is}\\
V = \cfrac{4\pi r^3}{3}\\
\text{and you have }\\
V = \cfrac{256 \pi}{3}\\
\text{thus then}\\
\cfrac{256 \pi}{3}= \cfrac{4\pi r^3}{3}\\
\text{solving for "r" then}\\
\cfrac{256 \pi}{3(4 \pi)}=\cfrac{r^3}{3}
\implies \cfrac{3(256 \pi)}{3(4 \pi)} = r^3\\
\cfrac{\cancel{3}(256 \cancel{\pi})}{\cancel{3}(4 \cancel{\pi})} = r^3
$$

so solving for "r", what would that give you?