Answer:
V=1884 Cubic mm
Step-by-step explanation:
We know that the volume of the Sphere is given by the formula
[tex]V= \pi r^2h[/tex]
Where r is the radius and h is the height of the cylinder
We are asked to determine the radius of the hollow cylinder , which will be the difference of the solid cylinder and the cylinder being carved out.
[tex]V=V_1-V_2[/tex]
[tex]V=\pi r_1^2 \times h-\pi r_2^2 \times h[/tex]
[tex]V=\pi \times h \times (r_1^2-r_2^2)[/tex]
Where
[tex]V_1[/tex] is the the volume of solid cylinder with radius [tex]r_1[/tex] and height h
[tex]V_2[/tex] is the volume of the cylinder being carved out with radius [tex]r_2[/tex] and height h
where
[tex]r_1 = 7[/tex] mm ( Half of the bigger diameter )
[tex]r_2 = 5[/tex] mm ( Half of the inner diameter )
[tex]h=25[/tex] mm
Putting these values in the formula for V we get
[tex]V=\pi \times 25\times (7^2-5^2)[/tex]
[tex]V=3.14 \times 25 \times(49-25)[/tex]
[tex]V=3.14 \times 25 \times 24[/tex]
[tex]V= 1884[/tex]
