Answer:
Part A) The radius of the cylinder is [tex]r=\sqrt{\frac{125}{3\pi}}\ cm[/tex]
Part B) The height of the 500 ml mark is [tex]12\ cm[/tex]
Part C) The height of the 250 ml mark is [tex]6\ cm[/tex]
Step-by-step explanation:
Part A) What is the radius of the cylinder?
we know that
The volume of a cylinder is equal to
[tex]V=\pi r^{2} h[/tex]
we have
[tex]V=1\ l=1,000\ ml=1,000\ cm^{3}[/tex]
[tex]h=24\ cm[/tex]
substitute and solve for r
[tex]1,000=\pi r^{2} (24)[/tex]
[tex]r^{2}=\frac{1,000}{24\pi}[/tex]
[tex]r=\sqrt{\frac{1,000}{24\pi}}\ cm[/tex]
simplify
[tex]r=\sqrt{\frac{125}{3\pi}}\ cm[/tex]
Part B) What is the height of the 500 ml mark?
using proportion
[tex]\frac{24}{1,000}\frac{cm}{ml}=\frac{x}{500}\frac{cm}{ml}\\ \\x=500*24/1,000\\\\x=12\ cm[/tex]
Part C) What is the height of the 250 ml mark?
using proportion
[tex]\frac{24}{1,000}\frac{cm}{ml}=\frac{x}{250}\frac{cm}{ml}\\ \\x=250*24/1,000\\\\x=6\ cm[/tex]
