Answer:
area of cross section of cylinder is [tex]9\pi[/tex] inch²
Step-by-step explanation:
Given : Cylinder is 7 inch tall and has a volume of [tex]63\pi[/tex]inches³.
We have to find the area of cross section of cylinder.
Area of cross section of cylinder = [tex]\pi r^2[/tex]
To find the cross section first find radius.
Given Volume of cylinder = [tex]63\pi[/tex]inches³
Also , Volume of cylinder = [tex]\pi r^2h[/tex]
Thus, [tex]\Rightarrow 63\pi=\pi r^2h[/tex]
[tex]\Rightarrow 63=r^2(7)[/tex]
Divide both side by 7, we get,
[tex]\Rightarrow 9=r^2[/tex]
On simplifying , we get,
[tex]\Rightarrow r=\pm 3[/tex]
Since, radius has to be positive, thus neglecting negative term.
Thus, radius of cylinder = 3 inch
Thus, area of cross section of cylinder = [tex]\pi r^2[/tex]
area of cross section of cylinder = [tex]\pi (3)^2=9\pi[/tex]
Thus, area of cross section of cylinder is [tex]9\pi[/tex] inch²
