Answer:
The formula for 'h' is [tex]\frac{S.A.}{2\pi r}-r[/tex].
The height of the cylinder is 3 in.
Step-by-step explanation:
Given,
Surface Area of Cylinder = 251.2 sq. in.
Radius = 5 in
We have to find out the height of the cylinder.
Solution,
We know that the Surface area of cylinder is given as;
[tex]Surface\ Area = 2\pi r(h+r)[/tex]
Here 'r' is the radius and 'h' is the height.
We have to solve this for 'h'.
[tex]\frac{S.A.}{2\pi r}=h+r\\\\h=\frac{S.A.}{2\pi r}-r[/tex]
Hence The formula for 'h' is [tex]\frac{S.A.}{2\pi r}-r[/tex].
Now we solve for 'h'.
Since [tex]h=\frac{S.A.}{2\pi r}-r[/tex]
On putting the given values, we get;
[tex]h=\frac{251.2}{2\times3.14\times5}-5=8-5=3\ in[/tex]
Hence The height of the cylinder is 3 in.
