Answer:
5 inches
Step-by-step explanation:
The formula to find the surface area of a cylinder is A = 2πrh + 2πr²
Since we need the height we will need to solve for h
- First we can subtract 2πr² from both sides to get A - 2πr² = 2πrh
- Then we can divide both sides by 2πr to get [tex]h=\frac{A-2\pi r^{2} }{2\pi r}[/tex]
Now we can plug in our known values and solve for h
- Here we were given the diameter, d, however this formula is in terms of the radius, r.
- The diameter is equivalent to double the radius, d = 2r
- Therefore the radius is equivalent to half the diameter, [tex]r=\frac{1}{2} d[/tex]
- Plugging in d to solve for r we get [tex]r=\frac{1}{2}(2)[/tex] which simplifies to r = 1
The two variables for this equation we have no obtained, A = 12π and r = 1, so we can plug them into our equation to solve for the height
- [tex]h=\frac{12\pi -2\pi (1)^{2} }{2\pi (1)}=h=\frac{12\pi -2\pi }{2\pi }=\frac{10\pi }{2\pi } =5[/tex]
- The height is 5 inches
