Question

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:

विकल्प

• 1 : 1

• 2 : 1

• `sqrt3 : 2`

• `2 : sqrt3`

Answer 1

`sqrt3 : 2`

Explanation:

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

Total surface area of sphere = 4πR²

Total surface area of hemisphere = 3πr²

Given: Since, total surface area of a sphere and a hemisphere is equal,

4πR² = 3πr²

`(R)^2/(r)^2 = 3/4`

`R/r = sqrt(3/4)`

= `sqrt3/2`

= `sqrt3 : 2`