Answer:
The height is 0.2003ft
Step-by-step explanation:
Given
[tex]Surface\ Area = 520[/tex]
[tex]Base\ Area = 254.34[/tex]
Required
The height of the cylinder
The base area of the cylinder is:
[tex]Base\ Area = \pi r^2[/tex]
This gives
[tex]254.34 = 3.14 * r^2[/tex]
Divide by 3.14
[tex]81 = r^2[/tex]
Take square root of both sides
[tex]r = \sqrt{81[/tex]
[tex]r = 9[/tex]
The surface area of a cylinder is:
[tex]Surface\ Area = 2\pi rh + 2\pi r^2[/tex]
This gives
[tex]520 = 2*3.14* 9h + 2*3.14* 9^2[/tex]
[tex]520 = 56.52h + 508.68[/tex]
Collect like terms
[tex]56.52h = 520 -508.68[/tex]
[tex]56.52h = 11.32[/tex]
Solve for h
[tex]h = 11.32/56.52[/tex]
[tex]h = 0.2003ft[/tex]
