Answer:
(B) 108π cm²
Step-by-step explanation:
When the quarter circle is revolved around the vertical axis, it creates a hemisphere. The total surface area of the figure will be that of the flat circular surface at the bottom plus that of the half-sphere at the top.
The surface area of a sphere is
... A = 4πr²
so, half that is
... curved area of hemisphere = 2πr²
The area of the circular bottom will be that of a circle:
... A = πr²
Together, the total surface area is ...
... total area = curved area + flat area
... total area = 2πr² + πr² = 3πr²
For r = 6 cm, this area is ...
... 3π(6 cm)² = 108π cm² . . . . . seems to correspond to (B)
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Comment on answer choices
Answer choices without units attached are simply wrong. Because the radius dimension is in cm, we can presume the area measure will be cm², but there is nothing in the problem statement or answer choices that confirms this is the case.
In any event, the offered answers are pure numbers, not areas at all.
