Melting a hemisphere of radius 7 cm, four small identical spheres are made. What is the radius of these spheres?
- A3 cm
- B3.5 cm
- C4 cm
- D4.5 cm
Solution & Step-by-step Explanation
Let the radius of the hemisphere be R=7 cm and the radius of each small sphere be r.
When the hemisphere is melted to form 4 identical spheres, their total volumes must be equal:
Volume of hemisphere=4×Volume of one sphere
3
2
πR
3
=4×(
3
4
πr
3
)
3
2
R
3
=
3
16
r
3
2R
3
=16r
3
R
3
=8r
3
Taking the cube root on both sides:
R=2r
Given R=7 cm:
7=2r⟹r=
2
7
=3.5 cm
When the hemisphere is melted to form 4 identical spheres, their total volumes must be equal:
Volume of hemisphere=4×Volume of one sphere
3
2
πR
3
=4×(
3
4
πr
3
)
3
2
R
3
=
3
16
r
3
2R
3
=16r
3
R
3
=8r
3
Taking the cube root on both sides:
R=2r
Given R=7 cm:
7=2r⟹r=
2
7
=3.5 cm