Assume a hemispherical dome, so its volume is ⅔πr³ and its surface area is 2πr², where r=radius.
Volume/surface area=⅔πr³/2πr²=r/3. Surface area=3×volume/r.
⅔πr³=5747.02, r=∛(5747.02×1.5/π)=14cm approx.
So surface area=5747.02×3/14=1231.5 sq cm approx.