Question

The school is trying to paint one side of the curved dividers as shown below for the computer lab. The can of paint is able to cover an area of 25ft^2. Will this be enough paint? Select the best answer.
Screenshot of diagram: http://prntscr.com/j99t13

Answer 1

We do not have straight sides so we need to use integration to solve this problem.

We will use method of vertical strips.
We divide the area A into thin vertical strips of width dx, height y2-y1 and integrate from x1 to x2.
Assuming that lower left angle of dividers is in position (0,0) we have:
y2=3
y1=0
x1=0
x2=8

$A= \int\limits^8_0 {(3-0)} \, dA \\ \\ A= \int\limits^8_0 {3} \, dA \\ \\ A=3*8-3*0=24 ft^{2}$

Area is lower than 25ft^2 so the can of paint is able to cover an area.