Calcular el volumen en m3 de la esfera en el que el área de uno de sus círculos maximos es 36pim2

Answer:The volume of the sphere is [tex]V=288\pi\ m^3[/tex]Step-by-step explanation:The question in English isCalculate the volume in m^3 of the sphere in which the area of one of its maximum circles is 36pi m^2we know thatThe radius of the maximum circle in the sphere is equal to the radius of the sphereStep 1Find the radius of the maximum circleThe 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 sphereThe 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]