Multiple choice

After dinner, my friend cut a spherical watermelon of radius 6 cm into 2 equal parts. The surface area of each of the final pieces generated is

  1. 108π cm2

  2. 144π cm2

  3. 36π cm2

  4. 216π cm2

  5. None of these
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A Correct answer
Explanation

Surface area of a sphere is 4*pi*r^2. Cutting it into two hemispheres creates two new circular faces, each with area pi*r^2. Total surface area of one piece = (1/2 * 4*pi*r^2) + pi*r^2 = 2*pi*r^2 + pi*r^2 = 3*pi*r^2. With r=6, area = 3 * pi * 36 = 108*pi.

AI explanation

When a sphere of radius 6 cm is cut into two equal hemispheres, the total surface area of each piece equals the curved surface area of the hemisphere plus the area of the flat circular base. The curved surface area is 2 times pi times r squared, which is 2 times pi times 36 to equal 72 pi, and the circular base area is pi times r squared, which is 36 pi. Adding these gives 72 pi plus 36 pi to equal 108 pi square cm.

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