The volume of an inflated spherical water balloon is \( 79,092 \pi \mathrm{mm}^{3} \). What is the radius of the inflated water balloon?
A. \( 17 \mathrm{~mm} \)
B. \( 13 \mathrm{~mm} \)
C. \( 78 \mathrm{~mm} \)
D. \( 39 \mathrm{~mm} \)

Answer

Expert–verified

Hide Steps

Answer

\( r = \sqrt[3]{\frac{3(79092 \pi)}{4 \pi}} = 13 \mathrm{~mm} \)

Steps

Step 1 ：\( V = \frac{4}{3} \pi r^3 \)

Step 2 ：\( r = \sqrt[3]{\frac{3V}{4 \pi}} \)

Step 3 ：\( r = \sqrt[3]{\frac{3(79092 \pi)}{4 \pi}} = 13 \mathrm{~mm} \)