Answer:
(2646 +110.25π) cm² ≈ 2992.4 cm²
Explanation:
The area of a sphere is 4 times the area of a circle with the same radius. Hence the area of a hemisphere will be 2 times the area of that circle. This means carving a hemispherical depression in the face of the cube will add an area that is equal to the area of the circular hole.
Of course the total surface area of a cube is 6 times the area of one square face. The area of a circle is ...
A = πr² = π(d/2)² = (π/4)d²
The total surface area of the carved cube is ...
S = 6·(21 cm)² + (π/4)·(21 cm)² = (441 cm²)(6 +π/4)
S ≈ 2992.36 cm²
The total surface area of the remaining block is about 2992.4 cm².