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Problem

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13 Nov 2021

Given information

The given information is 

The sphere has radius . The base of the pyramid is a regular

To determine: The height of the pyramid of minimum volume whose base is a square and whose base triangular faces are all tangents to the sphere.

Step-by-step explanation

Step 1.

Calculations:

Let the height of the Pyramid for minimum volume be .

Radius of the sphere is .

Therefore,

                     Where, Distance between the centre of sphere and cone of pyramid.

Let the side of the square base be

Area of the square base is

 

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