Multiple choice

A solid sphere of radius $r$ cm is bisected along two perpendicular planes. The total surface area (in$cm^{2}$) of the $4$ pieces formed, is?

  1. $4 \pi r^{2}$
  2. $6 \pi r^{2}$
  3. $8 \pi r^{2}$
  4. $12 \pi r^{2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A sphere has surface area 4*pi*r^2. Bisecting with two perpendicular planes creates 4 quadrants (like orange wedges). Each piece has the original curved surface (1/4 of 4*pi*r^2 = pi*r^2) plus two flat semi-circular faces (each area 1/2*pi*r^2). Total area per piece = pi*r^2 + pi*r^2 = 2*pi*r^2. Total for 4 pieces = 8*pi*r^2.

AI explanation

Cutting the solid sphere into four identical pieces along two perpendicular planes introduces four new flat circular faces. Since each new flat face has an area of pi*r^2, the total area of these four flat faces is 4*pi*r^2. Adding this to the original curved surface area of the sphere, which is 4*pi*r^2, gives a total surface area of 8*pi*r^2.

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