KnowledgeBoat Logo

Mathematics

If a sphere and a cube have equal surface areas, then the ratio of the diameter of the sphere to the edge of the cube is

  1. 1 : 2

  2. 2 : 1

  3. π:6\sqrt{π} : \sqrt{6}

  4. 6:π\sqrt{6} : \sqrt{π}

Mensuration

15 Likes

Answer

A sphere and a cube have equal surface area.

Let a be the edge of cube and r the radius of sphere.

⇒ 4πr2 = 6a2

⇒ π(2r)2 = 6a2

Since, d = 2r

⇒ πd2 = 6a2

⇒d2a2=6π⇒d2a2=6π⇒da=6π.\Rightarrow \dfrac{d^2}{a^2} = \dfrac{6}{π} \\[1em] \Rightarrow \sqrt{\dfrac{d^2}{a^2}} = \dfrac{\sqrt{6}}{\sqrt{π}} \\[1em] \Rightarrow \dfrac{d}{a} = \dfrac{\sqrt{6}}{\sqrt{π}}.

Hence, Option 4 is the correct option.

Answered By

2 Likes

Related Questions