The formula for surface area is #S = \pi r^2 + \pi rl# where #r# is the radius of the semicircle and #l# is the length of the hut. If the surface area is 600, what is #l#?

1 Answer
smendyka
Jan 19, 2018

See a solution process below:

Explanation:

We can substitute #600# for #S# and solve for #l#:

#600 = pir^2 + pirl#

#600/(color(red)(pi)color(blue)(r)) = (pir^2 + pirl)/(color(red)(pi)color(blue)(r))#

#600/(pir) = (pir^2)/(color(red)(pi)color(blue)(r)) + (pirl)/(color(red)(pi)color(blue)(r))#

#600/(pir) = (color(red)(cancel(color(black)(pi)))r^color(blue)(cancel(color(black)(2))))/(cancel(color(red)(pi))cancel(color(blue)(r))) + (color(red)(cancel(color(black)(pi)))color(blue)(cancel(color(black)(r)))l)/(cancel(color(red)(pi))cancel(color(blue)(r)))#

#600/(pir) = r + l#

#600/(pir) - color(red)(r) = r + color(red)(r) - l#

#600/(pir) - r = 0 + l#

#600/(pir) - r = l#

#l = 600/(pir) - r#

Or

#l = 600/(pir) - ((pir)/(pir) xx r)#

#l = 600/(pir) - (pir^2)/(pir)#

#l = (600 - pir^2)/(pir)#

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