a conical cavity as
shown in the figure
is melted and cast
into 4 identical solid
spheres. What is the
ratio of the radius of
one sphere and that
of the given solid?
r
Г
r
Answers
Answered by
0
Answer:
what is your question....
Answered by
7
Answer:
t is known that volume of a sphere=
3
4
πr
3
So, volume of the original sphere=
3
4
π×9
3
The sphereical ball of radius 9cm is melted and recasted into three sphereical ball.
So, volume of the original spherical balls=Total volumes of all the three balls.
⇒
3
4
π×9
3
=
3
4
π×1
3
+
3
8
π×9
3
+
3
4
πr
3
Divide both sides by
3
4
π we get
⇒9
3
=1
3
+8
3
+r
3
⇒r
3
=9
3
−8
3
−1
3
⇒r
3
=(9
3
−8
3
)−1
3
⇒r
3
=(9−8)(9
2
+9×8+8
2
)−1
⇒r
3
=1(9
2
+9×8+8
2
)−1
⇒r
3
=1(81+72+64)−1
⇒r
3
=217−1=216cm
⇒r=6cm
Thus, the radius of the third ball=6cm
Step-by-step explanation:
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