Answer:
[tex]h=7\sqrt{2} -4\sqrt{3}[/tex] cm
Step-by-step explanation:
Given,
Total surface are of cylinder = [tex]56\pi \sqrt{6} \ cm^2[/tex]
Radius= [tex]4\sqrt{3}\ cm[/tex]
We have to find [tex]'h'[/tex].
Using formula for,
Total surface area of cylinder
= [tex]2\pi rh+ 2\pi r^2\\2\pi r(h+r)[/tex]
Now plugging the corresponding values,
[tex]56\pi \sqrt{6} =2\pi r(h+r)\\56\pi \sqrt{6} =2\pi\times4\sqrt{3}(h+4\sqrt{3})\\7\sqrt{6} = \sqrt{3}(h+4\sqrt{3})\\7\sqrt{2} =(h+4\sqrt{3} )\\7\sqrt{2}-4\sqrt{3}=h\\ or\\h=7\sqrt{2}-4\sqrt{3} \ cm[/tex]
Therefore, the height in the required format is [tex]7\sqrt{2}-4\sqrt{3} \ cm[/tex]
