A sphere of radius 21 cm is cut into 8 identical pieces by making three mutually perpendicular cuts through its center (one along each axis). Find the total surface area of each piece (in cm2).
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Correct answer: A
Explanation
The correct answer is Option 1 i.e. 551.25π cm2.
Cut by three mutually perpendicular planes through the center → 8 identical pieces, each an octant of the sphere
Surface area of each piece = (1/8 of sphere's surface area) + 3 quarter-circles (inner flat faces where cut)
Sphere's surface area = 4πR2 = 4π(21)2 = 1764π cm2
One-eighth of the area = 1764π/8 = 220.5π cm2
Each flat face: Quarter circle area = 110.25π cm2
Area of three such faces = 3 × 110.25π = 330.75π cm2
Total surface area of one piece = 220.5π + 330.75π = 551.25π cm2