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

Answer:

The formula for 'h' is $\frac{S.A.}{2\pi r}-r$.

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;

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

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

We have to solve this for 'h'.

$\frac{S.A.}{2\pi r}=h+r\\\\h=\frac{S.A.}{2\pi r}-r$

Hence The formula for 'h' is $\frac{S.A.}{2\pi r}-r$.

Now we solve for 'h'.

Since $h=\frac{S.A.}{2\pi r}-r$

On putting the given values, we get;

$h=\frac{251.2}{2\times3.14\times5}-5=8-5=3\ in$

Hence The height of the cylinder is 3 in.