Answer:
[tex]V=7238.2[/tex] cubic units
Step-by-step explanation:
As
And we know that the circumference of a great circle = 2[tex]\pi[/tex]r
2[tex]\pi[/tex]r = 24[tex]\pi[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}2\pi[/tex]
[tex]\frac{2\pi r}{2\pi }=\frac{24\pi }{2\pi }[/tex]
[tex]r=12[/tex]
Using the formula to find the volume of the sphere
[tex]V\:=\frac{4}{3}\pi r^3[/tex]
[tex]V\:=\frac{4}{3}\pi \left(12\right)^3[/tex]
[tex]\mathrm{Multiply\:fractions}:\quad \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}[/tex]
[tex]V=\frac{4\pi 12^3}{3}[/tex]
[tex]=\frac{2^6\cdot \:3^3\cdot \:4\pi }{3}[/tex] ∵ [tex]\mathrm{Factor}\:12^3:\quad 2^6\cdot \:3^3[/tex]
[tex]\mathrm{Cancel\:the\:common\:factor:}\:3[/tex]
[tex]V=2^6\cdot \:3^2\cdot \:4\pi[/tex]
[tex]V=3^2\cdot \:64\cdot \:4\pi[/tex]
[tex]V=64\cdot \:9\cdot \:4\pi[/tex]
[tex]V=2304\pi[/tex]
[tex]V=7238.2[/tex] cubic units
