Final answer:
The surface area of the sphere is approximately 1963.495 cm², calculated using the formula A = 4 π r² where the radius is half the cube's side, i.e., 12.5 cm.
Step-by-step explanation:
The subject is mathematics, specifically geometry, and the question pertains to calculating the surface area of a sphere that fits into a cube. We start by noting that the diameter of the sphere is equal to the side of the cube. Since the side of the cube is given as 25 cm, this is also the diameter of the sphere, so the radius, r, is 12.5 cm. The surface area, A, of a sphere can be calculated using the formula A = 4 π r². Plugging in the value for the radius:
A = 4 π (12.5 cm)²
A = 4 π (156.25 cm²)
A = 4 π × 156.25 cm²
A ≈ 4 × 3.14159 × 156.25 cm²
A ≈ 1963.495 cm²
The approximate surface area of the sphere is therefore 1963.495 cm².