5. The volume of a sphere is $2304 \pi \mathrm{cm}^{3}$. Determine the radius using the formula $r=\sqrt[3]{\frac{3 V}{4 \pi}}$, where $V$ is the volume in cubic units and $r$ is the radius.
A $8 \mathrm{~cm}$
B $12 \mathrm{~cm}$
C $42 \mathrm{~cm}$
D $1728 \mathrm{~cm}$
Answer
Final Answer: \(\boxed{12 \mathrm{~cm}}\)
Step 1 ：We are given the volume of the sphere and need to find the radius using the given formula. We can plug in the given volume into the formula and solve for the radius.
Step 2 ：volume = 2304 \(\pi\) cm^3
Step 3 ：radius = \(\sqrt[3]{\frac{3 V}{4 \pi}}\)
Step 4 ：radius = \(\sqrt[3]{\frac{3 \times 2304 \pi}{4 \pi}}\)
Step 5 ：radius = \(\sqrt[3]{\frac{6912 \pi}{4 \pi}}\)
Step 6 ：radius = \(\sqrt[3]{1728}\)
Step 7 ：radius = 12 cm
Step 8 ：Final Answer: \(\boxed{12 \mathrm{~cm}}\)
