To determine the radius of a sphere given its volume, we use the formula for the volume of a sphere:
\(\[ V = \frac{4}{3} \pi r^3 \]\)
Given that the volume \(\( V \)\) is \(\( 36\pi \)\) cubic units, we can set up the equation:
\(\[ 36\pi = \frac{4}{3} \pi r^3 \]\)
To solve for the radius \(\( r \)\), we follow these steps:
1. Isolate the \(\( r^3 \)\) term:
Divide both sides of the equation by \(\( \pi \)\):
\(\[ 36 = \frac{4}{3} r^3 \]\)
2. Eliminate the fraction:
Multiply both sides by \(\( 3 \)\) to get rid of the denominator:
\(\[ 36 \times 3 = 4 r^3 \]\)
\(\[ 108 = 4 r^3 \]\)
3. Solve for \(\( r^3 \)\):
Divide both sides by \(\( 4 \)\):
\(\[ r^3 = \frac{108}{4} \]\)
\(\[ r^3 = 27 \]\)
4. Take the cube root:
Solving for \(\( r \)\) involves taking the cube root of both sides:
\(\[ r = \sqrt[3]{27} \]\)
\(\[ r = 3 \]\)
Thus, the radius of the sphere is 3 units.
So, the correct option is:
O 3 units
