Question

Find the surface area of a cylinder. Solve this formula for h. Then find the height of the cylinder if the surface are is 251.2 in2 and the radius is 5 in.

Answer 1

The formula for 'h' is
`(S.A.)/(2\pi r)-r`.

The height of the cylinder is 3 in.

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;

`Surface\ Area = 2\pi r(h+r)`

Here 'r' is the radius and 'h' is the height.

We have to solve this for 'h'.

`(S.A.)/(2\pi r)=h+r\\\\h=(S.A.)/(2\pi r)-r`

Hence The formula for 'h' is
`(S.A.)/(2\pi r)-r`.

Now we solve for 'h'.

Since
`h=(S.A.)/(2\pi r)-r`

On putting the given values, we get;

`h=(251.2)/(2*3.14*5)-5=8-5=3\ in`

Hence The height of the cylinder is 3 in.