Multiple choice

If $ \displaystyle S_{1} $ and $\displaystyle S_{2} $ be the whole surface of a sphere and the curved surface of the circumscribed cylinder then $ \displaystyle S_{1} $ is equal to

  1. $ \displaystyle S_{2} $
  2. $ \displaystyle 2S_{2} $
  3. $ \displaystyle \frac{1}{2}S_{2} $
  4. $ \displaystyle \frac{2}{3}S_{2} $
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A Correct answer
Explanation

Surface area of sphere S1 = 4*pi*r^2. Circumscribed cylinder has height h = 2r and radius r. Curved surface area S2 = 2*pi*r*h = 2*pi*r*(2r) = 4*pi*r^2. Thus S1 = S2.

AI explanation

For a sphere of radius r, the total surface area S1 is given by the formula 4*pi*r^2. The radius of the circumscribed cylinder equals the radius of the sphere and its height is 2r, so the curved surface area S2 of the cylinder is 2*pi*r*(2r) = 4*pi*r^2. Comparing both results, S1 is equal to S2.

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