Question #5acf9

2 Answers
Jan 3, 2018

r=3.1987 cm

Explanation:

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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

Jan 3, 2018

r =color(blue)( 3.198 cm)

Explanation:

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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