13 Nov 2021
Problem 22
Page 329
Section: Focus on Problem Solving
Chapter 4: Applications of Differentiation
Textbook ExpertVerified Tutor
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