The radius of exercise ball is 0.5 meter, if Billy’s exercise ball contains 0.523 [tex]m^{3}[/tex] of air and [tex]\pi[/tex] = 3.14.
Step-by-step explanation:
The given is,
Volume of exercise ball = 0.523 cubic meter
Step:1
Exercise ball looks like a sphere,
Formula foe volume of sphere,
[tex]Volume, V = \frac{4}{3} \pi r^{3}[/tex]......................(1)
Where, r - Radius of sphere
From given, V = 0.523 cubic meters
Equation (1) becomes,
[tex]0.523 = \frac{4}{3} \pi r^{3}[/tex]
[tex]0.523 = \frac{4}{3} (3.14) r^{3}[/tex] (∵ [tex]\pi[/tex] = 3.14 )
[tex]0.523 = (1.333)(3.14)r^{3}[/tex]
[tex]0.523 = (4.18667)r^{3}[/tex]
[tex]r^{3} = \frac{0.523}{4.18667}[/tex]
[tex]r^{3} = 0.12492[/tex]
Take cube root on both sides,
[tex]r=\sqrt[3]{0.12492}[/tex]
r = 0.49989
r ≅ 0.5 meter
Result:
The radius of exercise ball is 0.5 meter, if Billy’s exercise ball contains 0.523 [tex]m^{3}[/tex] of air and [tex]\pi[/tex] = 3.14.
