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Since the surface area of this cylinder is [tex]432\pi \;yd^2[/tex], its diameter is equal to 12 yards.
Mathematically, the surface area (SA) of a cylinder is given by this formula:
[tex]S.A = 2\pi rh + 2\pi r^2[/tex]
Where:
Given the following data:
Substituting the given parameters into the formula, we have;
[tex]432\pi = 2\pi r(5r) + 2\pi r^2\\\\432\pi = 2\pi 5r^2 + 2\pi r^2\\\\216=5r^2+r^2\\\\216=6r^2\\\\r^2=36\\\\r=\sqrt{36}[/tex]
r = 6 yards.
For the diameter:
Diamter = 2 x radius
Diamter = 2 x 6
Diameter = 12 yards.
Read more on surface area here: brainly.com/question/21367171