Answer:
946.808 cm²
Explanation:
The figure is made up of a cone and a hemisphere.
Volume of a cone is given as;
V_c = ⅓πr²h
Volume of a hemisphere is given as;
V_h = ⅔πr³
In the figure, radius of hemisphere is 6.
Thus; V_h = ⅔π × 6³ = 452.389 cm²
For the cone, height is not given but we can find it from pythagoras theorem.
h = √(6² + (2√(34))²
h = √(36 + (4 × 34))
h = √(172)
Thus;
V_c = ⅓π × 6² × √(172)
V_c = 494.419 cm²
Total area = V_c + V_h = 494.419 + 452.389 = 946.808 cm²