Homework SourseGiven a sphere with radius find the height of a pyramid of
Given a sphere with radius , find the height of a pyramid of minimum volume whose base is
a square and whose base and triangular faces are all tangent to the sphere. What if the base of
the pyramid is a regular n-gon? (A regular n-gon is a polygon with equal sides and angles.)
(Use the fact that the volume of a pyramid is 1/3(A)(h), where A is the area of the base.)
a square and whose base and triangular faces are all tangent to the sphere. What if the base of
the pyramid is a regular n-gon? (A regular n-gon is a polygon with equal sides and angles.)
(Use the fact that the volume of a pyramid is 1/3(A)(h), where A is the area of the base.)
Solution
if the base is a square , then each side of square be x
=> x/(23) = r ,radius of sphere
=> height = x3/2
=> height = 3r
do similarly if base is a regular polygon
