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A solid metal sphere of radius 21 cm is cut into two identical hemispheres. What is the combined total surface area of the two hemispheres, in square cm? (Use π = 22/7.)

Competition practiceMensuration
  • A2772
  • B4158
  • C5544
  • D8316

Step-by-Step Solution

Here π sq cm. Each solid hemisphere has a curved part 2π plus a flat circular face π, i.e. 3π sq cm, so the two together give 6π sq cm. The trap 5544 is the sphere's own surface 4π, which ignores that cutting exposes two new circular faces; 4158 gives only one hemisphere; 2772 is the pair of new flat faces alone, 2π, the increase rather than the total.
Answer: D) 8316

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