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# A cylinder has a surface area of 3000sqft. Its length is six times its diameter. How long is the cylinder?

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- cidyahLv 71 decade agoFavorite Answer
Surface area = 2PI r h + 2 PI r^2 =3000

h = 12r ( 6 times the diameter means 12 times the radius)

r = h/12

Surface area = 2PI (h/12) h + 2PI (h/12)^2 = 3000

PI h^2 / 6 + PI h^2 / 72 = 3000

12 PI h^2 / 72 + PI h^2 / 72 = 3000

13 PI h^2 / 72 = 3000

13 PI h^2 = (3000)(72)=216 000

PI h^2 = 16615.3846

h^2 = 16615.3846 / PI

h = 128.9 / sqrt(PI)

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