MathDB

region closer to one vertex than other vertices of cube

Source: Putnam 1983 B1

September 15, 2021

geometry3D geometryVolumeintegrationcalculus

Problem Statement

Let

v

be a vertex of a cube

C

with edges of length

4

. Let

S

be the largest sphere that can be inscribed in

C

. Let

R

be the region consisting of all points

p

between

S

and

C

such that

p

is closer to

v

than to any other vertex of the cube. Find the volume of

R