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Answer 1 · 2018-01-03T04:34:01

#r=3.1987# #cm#

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The formula for surface area of a cylinder is:

#Surface Area_("cylinder")=2pirh+2pir^2#

In this problem,

#h=10d=10(2r)=20r#

We substitute this in the formula:

#A=2pir(20r)+2pir^2=1350#

#40pir^2+2pir^2=1350#

#42pir^2=1350#

#r^2=1350/(42pi)#

#r=sqrt((1350)/(42pi))=3.1987# #cm#

Answer 2 · 2018-01-03T05:06:27

#r =color(blue)( 3.198 cm)#

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General equation for the Total Surface Area of a cylinder is

#A = 2 pi r^2 + 2 pi r h #

# r^2 + rh = A / (2 pi)#

#r^2 + h r - (A / (2 pi)) = 0#

Formula to find roots of a quadratic equation
#ax^2 + b x c = 0# is given by

#x = (-b +- sqrt(b^2 + 4 a c)) / (2a)#

#:. r = ( - h +- sqrt(h^2 + ((4A)/( 2 pi)))) / 2#

#r = (-h +- sqrt(h^2 + ((2A) / (pi)))) / 2#

In this problem,
#A = 1350, h = 10 d = 20r#

#:.1350 = 2pir^2 + 2pirh = 2pi(r^2 + r * 20r)#

#2 pir^2 (1 + 20) = 1350#

#r^2 = 1350 / (2pi * 21)#

#r^2 = 1350 / ((2 * 22 * cancel(color (red)(21) )3 )/cancel(color(red)(7))) = 1350 / 132#

#r = sqrt(1350/132) = 3.198 cm#