A hemisphere of lead of radius 7/2 cm is cast into a right circular cone of height 49/2cm. Find the base radius of the cone.
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Answer:
Given,
Radius of hemispher R=7 cm
Hight of cone h=49 cm
Volume of hemisphere V=
3
2
πR
3
=
3
2
π×(7)
3
cm
3
=
3
2
×343×π cm
3
=
3
686
π cm
3
Volume of cone V=
3
1
πr
2
h
=
3
1
πr
2
×49 cm
The hamisphere is cast into a right circular cone of hight (h=49 cm) and have base radius r.
→Volume of hemisphere = Volume of cone
3
686
π cm
3
=
3
49
πr
2
cm
r
2
=
49
686
cm
2
r
2
=14 cm
2
r= 14
cm
Hence, radius of base of cone r=3.74 cm
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