Answer:
[tex]r=\frac{1}{4}\text{ m}=0.25\text{ m}[/tex]
Step-by-step explanation:
We have been given that volume of a sphere is [tex]\frac{1}{48}\pi\text{ m}^3[/tex]. We are asked to find the length of sphere's radius.
To find the radius of sphere we will use volume of sphere formula.
[tex]\text{Volume of sphere}=\frac{4}{3}\pi r^3[/tex], where r represents the radius of sphere.
Upon substituting our given volume in above formula we will get,
[tex]\frac{1}{48}\pi\text{ m}^3=\frac{4}{3}\pi r^3[/tex]
Let us multiply both sides of our equation by 3/4.
[tex]\frac{3}{4}\times\frac{1}{48}\pi\text{ m}^3=\frac{3}{4}\times\frac{4}{3}\pi r^3[/tex]
[tex]\frac{\pi}{4\times 16}\text{ m}^3=\pi r^3[/tex]
Dividing both sides of our equation by pi we will get,
[tex]\frac{\pi}{64\pi}\text{ m}^3=\frac{\pi r^3}{\pi}[/tex]
[tex]\frac{1}{64}\text{ m}^3=r^3[/tex]
Taking cube root of both sides of our equation we will get,
[tex]\sqrt[3]{\frac{1}{64}\text{ m}^3}=r[/tex]
[tex]\sqrt[3]{\frac{1}{4^3}\text{ m}^3}=r[/tex]
[tex]\frac{1}{4}\text{ m}=r[/tex]
[tex]r=\frac{1}{4}\text{ m}=0.25\text{ m}[/tex]
Therefore, the radius of sphere is 0.25 meters.
