Respuesta :
Answer:
the radius of the inflated balloon is: [tex]r=34.822\,\text{mm}[/tex]
Step-by-step explanation:
Since it is stated that the water balloon has a spherical shape: We can confidently use the formula for the volume of a sphere to calculate the radius.
Volume is denoted as 'V' and radius is denoted as 'r'.
[tex]V=\dfrac{4}{3}\pi r^3[/tex]
Volume is 176,868 mm^3
[tex]176868=\dfrac{4\pi r^3}{3}[/tex]
Now we can solve for the radius r.
[tex]\dfrac{3}{4\pi}(176868)=r^3[/tex]
[tex]\dfrac{3(176868)}{4\pi}=r^3[/tex]
[tex]\dfrac{132651}{\pi}=r^3[/tex]
cube root both sides
[tex]\sqrt[3]{\dfrac{132651}{\pi}}=\sqrt[3]{r^3}[/tex]
[tex]r= \dfrac{51}{\sqrt[3]{\pi}}\approx34.822\,\text{mm}[/tex]
the radius of the inflated balloon is: [tex]r=34.822\,\text{mm}[/tex]
