Three hemisphere of gold whose radi are 2cm, 12cm, and 16cm respectively are melted to form a single hemisphere. What is the radius of new hemisphere?
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Answer:
r
1
=2,r
2
=12,r
3
=16
Spheres of radii r
1
,r
2
,r
3
are melted into a sphere of radius r
0
∴
3
4
πr
1
3
+
3
4
πr
2
3
+
3
4
πr
3
3
=
3
4
πr
0
3
=>r
0
3
=r
1
3
+r
2
3
+r
3
3
=>r
0
3
=2
3
+12
3
+16
3
=>r
0
=18
Therefore, radius of the new sphere is 18cm.
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