The area of the circular base of a cylinder is 367 square units. The height of the cylinder is 2 units. What is the lateral area of the cylinder? Express the answer in terms of …

Question

asked Jan 26, 2021 4.6k views

1 Answer

John Rice · Answer 1 · 2021-01-29T16:01:30+0000

Answer:

A=135.82u^2

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:

$(367u^2)/(\pi)=r^2\\\\\sqrt{(367u^2)/(\pi ) }=r\\\\\sqrt{(367u^2)/(3.1416) }=r\\\\10.808u=r$

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:

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