Question

The area of the circular base of a cylinder is 367 square units. The height of the cylinder is 2 units.

Answer 1

Answer:

$A=135.82u^2$

Step-by-step explanation:

The formula to calculate the lateral area of a cylinder is:

$A=h*c$

where h is the height of the cylinder, and c is the circumference (perimeter) of the circular base:

$c=2\pi r$ 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:

$367u^2$,

substituting this in the formula for the area of a circle:

$A_{c}=\pi r^2$

$367u^2=\pi r^2$

and solving for the radius:

$\frac{367u^2}{\pi}=r^2\\\\\sqrt{\frac{367u^2}{\pi } }=r\\\\\sqrt{\frac{367u^2}{3.1416} }=r\\\\10.808u=r$

now that we know the radius, we calculate the circumference:

$c=2\pi r\\c=2\pi (10.808u)\\c=67.91u$

and finally we go back to the formula for the lateral area:

$A=h*c$

and substitute the height: $h=2u$ and the circumference:

$A=(2u)(67.91)\\A=135.82u^2$