Question

How do i answer this please?!

Answer 1

`h=7√(2) -4√(3)` cm

Explanation:

Given,

Total surface are of cylinder =
`56\pi √(6) \ cm^2`

Radius=
`4√(3)\ cm`

We have to find
`'h'`.

Using formula for,

Total surface area of cylinder

=
`2\pi rh+ 2\pi r^2\\2\pi r(h+r)`

Now plugging the corresponding values,

`56\pi √(6) =2\pi r(h+r)\\56\pi √(6) =2\pi*4√(3)(h+4√(3))\\7√(6) = √(3)(h+4√(3))\\7√(2) =(h+4√(3) )\\7√(2)-4√(3)=h\\ or\\h=7√(2)-4√(3) \ cm`

Therefore, the height in the required format is
`7√(2)-4√(3) \ cm`