Question

find the volume of the largest right circular cone that can be cut out of the cube whose edges is 21​

Answer 1

The base of the largest right circular cone will be the circule inscribed in a face of the cube and its height will be equal to an edge of the cube
∴
∴
radius of the base of the cone, r=212cm
r
=
21
2
c
m

and height of the cone, h=21cm
h
=
21
c
m

∴
∴
volume of the required cone
=13πr2h
=
1
3
π
r
2
h

=(13×227×212×212×21)cm3
=
(
1
3
×
22
7
×
21
2
×
21
2
×
21
)
c
m
3

=48512cm3=2425.5cm3
=
4851
2
c
m
3
=
2425.5
c
m
3