Question No: 13
A solid cylinder with
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?
Answers
Given : A solid cylinder with a conical cavity is melted and cast
into 4 identical solid spheres
To Find : ratio of the radius of one sphere and that of the given solid
Solution:
Radius of cylinder = r
Volume of cylinder = πr²h
Volume of conical cavity = (1/3)πr²h
Hence Volume = πr²h - (1/3)πr²h = (2/3)πr²h
melted and cast into 4 identical solid spheres
Radius of Sphere = R
Volume of one sphere = (4/3) πR³
=> Volume of 4 spheres = 4 * (4/3) πR³ = (16/3) πR³
(16/3) πR³ = (2/3)πr²h
=> 8R³ = r²h
Height of cylinder also needed to find ratio of radius
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Answer:
1:2
Step-by-step explanation:
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