Answer:
The volume of the container is [tex]38,772.72\ cm^{3}[/tex]
Step-by-step explanation:
step 1
Find the radius of the sphere
we know that
The surface area of a sphere is equal to
[tex]SA=4\pi r^{2}[/tex]
we have
[tex]SA=5,538.96\ cm^{2}[/tex]
[tex]\pi=3.14[/tex]
substitute the values and solve for r
[tex]5,538.96=4(3.14)r^{2}[/tex]
[tex]r^{2}=5,538.96/[4(3.14)][/tex]
[tex]r^{2}=441[/tex]
[tex]r=21\ cm[/tex]
step 2
Find the volume of the container
The volume of the sphere (container) is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
we have
[tex]r=21\ cm[/tex]
[tex]\pi=3.14[/tex]
substitute the values
[tex]V=\frac{4}{3}(3.14)(21)^{3}=38,772.72\ cm^{3}[/tex]
Answer:
For the first part it would be 38772.72 cm^3 and for the second part it would be 65 minutes to fill the container.
