a spherical container has surface area of about 5,538.96 square centimeters. what is the volume lf the container? use 3.14 for pi, and round to the nearest hundredth
Accepted Solution
A:
Answer:The volume of the container is [tex]38,772.72\ cm^{3}[/tex]Step-by-step explanation:step 1Find the radius of the spherewe know thatThe 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 2Find the volume of the containerThe 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]