Respuesta :
Answer:
Step-by-step explanation:
cylinder's height=3×(diameter of sphere)=3×6=18 cm
radius of cylinder=3 cm
volume of cylinder=π r²h=π(3)²×18=162 π cm³
volume of sphere=4/3 π(3)³=36 π cm³
reqd. empty space=162 π-3×36π=54 πcm³
The amount of empty space within a cylinder containing three solid spheres would be 54 πcm³.
What is the volume of a right circular cylinder?
Suppose that the radius of considered right circular cylinder be 'r' units.
And let its height be 'h' units.
Then, its volume is given as:
[tex]V = \pi r^2 h \: \rm unit^3[/tex]
Each sphere has a radius of 3 cm
We can assume the cylinder height to the 3 times the diameter of the sphere.
The cylinder's height = 3 × (the diameter of the sphere)
= 3 × 6 =18 cm
The radius of cylinder = 3 cm
The volume of cylinder = π r²h
= π(3)² × 18
= 162 π cm³
The volume of sphere = 4/3 π(3)³
=36 π cm³
The amount of empty space within a cylinder containing three solid spheres,
= 162 π - 3 × 36π
= 54 πcm³
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