Answer:
[tex]A=135.82u^2[/tex]
Step-by-step explanation:
The formula to calculate the lateral area of a cylinder is:
[tex]A=h*c[/tex]
where h is the height of the cylinder, and c is the circumference (perimeter) of the circular base:
[tex]c=2\pi r[/tex] where r is the radius
To calculate the circumference we need the radius of the circle, which we can calculate because we know that the area the circle is:
[tex]367u^2[/tex],
substituting this in the formula for the area of a circle:
[tex]A_{c}=\pi r^2[/tex]
[tex]367u^2=\pi r^2[/tex]
and solving for the radius:
[tex]\frac{367u^2}{\pi}=r^2\\\\\sqrt{\frac{367u^2}{\pi } }=r\\\\\sqrt{\frac{367u^2}{3.1416} }=r\\\\10.808u=r[/tex]
now that we know the radius, we calculate the circumference:
[tex]c=2\pi r\\c=2\pi (10.808u)\\c=67.91u[/tex]
and finally we go back to the formula for the lateral area:
[tex]A=h*c[/tex]
and substitute the height: [tex]h=2u[/tex] and the circumference:
[tex]A=(2u)(67.91)\\A=135.82u^2[/tex]
