Multiple choice

The radius of a solid sphere is 'r' cm. It is bisected, then the total surface area of the two pieces obtained is

  1. $8\pi r^2 cm^2$
  2. $4\pi r^2 cm^2$
  3. $5\pi r^2 cm^2$
  4. $6\pi r^2 cm^2$
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D Correct answer
Explanation

A solid sphere has a surface area of 4*pi*r^2. When bisected, two hemispheres are created. Each hemisphere has a curved surface area of 2*pi*r^2 and a flat circular base of pi*r^2, totaling 3*pi*r^2 per piece. For two pieces, the total surface area is 6*pi*r^2.

AI explanation

The total surface area of a sphere is given by 4 times pi times the radius squared, and when the sphere of radius r is bisected, two new flat circular faces are created. The area of each new flat circular face is pi times r squared, adding 2 times pi times r squared to the total area. Adding the original curved surface area of 4 times pi times r squared to the 2 times pi times r squared of the two new faces results in a total surface area of 6 times pi times r squared.

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