Answer:
The volume inside the cylinder is [tex]1152\pi\ cm^3[/tex].
Step-by-step explanation:
Given : Four spheres of radius 6 cm just fit inside a cylinder.
To find : Calculate the volume inside the cylinder that is empty ?
Solution :
The volume of the cylinder is volume of 4 spheres.
The volume of sphere is [tex]V=\frac{4}{3}\pi r^3[/tex]
The radius is 6 cm.
The volume of four spheres is
[tex]V=4\times \frac{4}{3}\times \pi\times (6)^3[/tex]
[tex]V=1152\pi\ cm^3[/tex]
Therefore, the volume inside the cylinder is [tex]1152\pi\ cm^3[/tex].
The volume inside the cylinder that is empty will be [tex]3883.76\pi[/tex].
Given information:
Four spheres of radius 6cm just fit inside a cylinder.
The sphere just fits the cylinder. So, the height of the cylinder will be equal to 2 times the diameter of the sphere.
Radius R of the cylinder will be calculated as,
[tex]R=\dfrac{\sqrt2\times 12+6+6}{2}\\R=6\sqrt2+6[/tex]
Based on the above conclusion:
Now, the volume of the cylinder will be,
[tex]V_c=\pi r^2h\\V_c=\pi (6\sqrt2+6)^2\times 24\\V_c=5035.76\pi[/tex]
The volume of sphere will be,
[tex]V_s=\dfrac{4}{3}\pi r^3\\V_s=288\pi[/tex]
So, the volume of empty space will be,
[tex]V_c-4V_s=5035.76\pi-4\times288\pi\\V=3883.76\pi[/tex]
Therefore, the volume inside the cylinder that is empty will be [tex]3883.76\pi[/tex].
For more details, refer to the link:
https://brainly.com/question/22441665
