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The total surface area of a solid sphere (S1) and a solid hemisphere (S2), as shown in the diagram, are equal. The ratio of radii R and r is :

The total surface area of a solid sphere and a solid hemisphere, as shown in the diagram, are equal. The ratio of radii R and r is. ICSE 2026 Maths Solved Question Paper.

  1. 1 : 1

  2. 2 : 1

  3. 3\sqrt3 : 2

  4. 2 : 3\sqrt3

Mensuration

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Answer

Let the radius of the sphere (S1) be R and hemisphere (S2) be r.

Total surface area of sphere = 4πR2

Total surface area of hemisphere = 3πr2

Given,

Since, total surface area of sphere and hemisphere are equal,

4πR2 = 3πr2

R2r2=34\dfrac{R^2}{r^2} = \dfrac{3}{4}

Rr=34=32=3:2\dfrac{R}{r} = \sqrt{\dfrac{3}{4}} = \dfrac{\sqrt{3}}{2} = \sqrt{3} : 2.

Hence, option 3 is the correct option.

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