Answer:
The volume of the sphere is [tex]V=288\pi\ m^3[/tex]
Step-by-step explanation:
The question in English is
Calculate the volume in m^3 of the sphere in which the area of one of its maximum circles is 36pi m^2
we know that
The radius of the maximum circle in the sphere is equal to the radius of the sphere
Step 1
Find the radius of the maximum circle
The area of the circle is
[tex]A=\pi r^{2}[/tex]
we have
[tex]A=36\pi\ m^2[/tex]
substitute and solve for r
[tex]36\pi=\pi r^{2}[/tex]
Simplify
[tex]36=r^{2}[/tex]
take the square root both sides
[tex]r=6\ m[/tex]
Step 2
Find the volume of the sphere
The volume of the sphere is
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
substitute the value of r
[tex]V=\frac{4}{3}\pi (6)^{3}[/tex]
[tex]V=288\pi\ m^3[/tex]
