Question

How do i answer this please?!

Answer 1

Answer:

$h=7\sqrt{2} -4\sqrt{3}$ cm

Step-by-step explanation:

Given,

Total surface are of cylinder = $56\pi \sqrt{6} \ cm^2$

Radius= $4\sqrt{3}\ cm$

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,

$56\pi \sqrt{6} =2\pi r(h+r)\\56\pi \sqrt{6} =2\pi\times4\sqrt{3}(h+4\sqrt{3})\\7\sqrt{6} = \sqrt{3}(h+4\sqrt{3})\\7\sqrt{2} =(h+4\sqrt{3} )\\7\sqrt{2}-4\sqrt{3}=h\\ or\\h=7\sqrt{2}-4\sqrt{3} \ cm$

Therefore, the height in the required format is $7\sqrt{2}-4\sqrt{3} \ cm$