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Consider the following statements, which of them is/are correct? I. If the height of cylinder is doubled, the area of curved surface is doubled. II. If the radius of a hemispherical solid is…

Question and options

Consider the following statements, which of them is/are correct?

I. If the height of cylinder is doubled, the area of curved surface is doubled.
II. If the radius of a hemispherical solid is doubled, its total surface area becomes fourfold.
III. If a hemisphere and cone have equal bases and equal heights, then the ratio of their curved surface areas (hemisphere : cone) is 2:1\sqrt{2}:1.
  1. II and III only
  2. I and III only
  3. I and II only
  4. I, II and III

Answer and explanation

Correct answer: D - I, II and III
I: CSA = 2*pi*r*h doubles when h doubles, true. II: hemisphere TSA = 3*pi*r^2, so doubling r makes it 4 times, true. III: equal base radius r and equal height means the cone height is r, slant = r*sqrt2, cone CSA = sqrt2*pi*r^2, hemisphere CSA = 2*pi*r^2, so hemisphere : cone = 2 : sqrt2 = sqrt2 : 1, true. All three are correct.

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