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Guided Example #1 - Three-Dimensional Geometry

If the volume of a right circular cylinder is 1280 Π cubic feet and the ratio of height to radius is 5:2, what is the total surface area?

Step 1

h:r = 5:2
Let h = 5x and r = 2x
V =

$Π r^{2} h$

Step 2

So $Π {(2 x)}^{2} (5 x) = 1280 Π$
$20 x^{3} = 1280$
$x^{3} = 64$
x = 4, h = 20, and r = 8

Step 3

Total Surface Area

$= 2 Π r h + 2 (Π r^{2})$

$= 2 Π x 8 x 20 + 2 x Π x 8^{2}$

$= 320 Π + 128 Π$

$= 448 Π square f e e t$

All Steps

h:r = 5:2
Let h = 5x and r = 2x
V =

$Π r^{2} h$

So

$Π {(2 x)}^{2} (5 x) = 1280 Π$

$20 x^{3} = 1280$

$x^{3} = 64$
x = 4, h = 20, and r = 8

Total Surface Area

$= 2 Π r h + 2 (Π r^{2})$

$= 2 Π x 8 x 20 + 2 x Π x 8^{2}$

$= 320 Π + 128 Π$

$= 448 Π square f e e t$