Let r1 and h be the radius and height of the upper cone.
Let r2 be the radius of the bigger cone.
Let v1 & v2 be the volumes of upper cone and bigger cone respectively.
Now, v1=164v2
⇒13πr21h=164×13πr22×40
⇒(r1r2)2=40641h→(1).
△ADE∼△ABC thus
ADAB=DEBC⇒h40=r1r2→(2).
From (1) and (2), we get,
(h40)2=4064×1h
⇒h3=40×40×404×4×4
⇒h=3√40×40×404×4×4
⇒h=404=10cm.
Height of upper cone=10cm.
At (40−10=30cm) above the base the section is made.