A cubical box is placed in a hemisphere, find a relation between radius of hemisphere and side of cube.

Given:

A cubical box is placed in a hemisphere.

To do:

We have to find the relation between the radius of the hemisphere and the side of the cube.

Solution:

Let the radius of the hemisphere be $r$ and the side of the cube be $s$.

The diagonal of the face of the cube $=$ Diameter of the hemisphere

Therefore,

$\sqrt{s^2+s^2}=2\times r$

$2\sqrt{s}=2r$

$\sqrt{s}=r$

$s=r^2$     (Squaring on both sides) 

The relation between the radius of the hemisphere and the side of the cube is the side of the square is equal to the radius squared.

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Updated on: 10-Oct-2022

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