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Answer:
Step-by-step explanation:
let r be radius of the cylinder.
volume of cylinder=πr²h
1728π=πr²×12
r²=1728 π/12π=144
r=√144=12
diameter=2r=2×12=24 cm
Answer:
[tex]\boxed {\boxed {\sf 24 \ centimeters}}}[/tex]
Step-by-step explanation:
The volume of a cylinder is found using this formula:
[tex]V= \pi r^2 h[/tex]
We know the height is 12 centimeters and the volume is 1728π cubic centimeters. We can substitute the values into the formula.
[tex]1728 \pi \ cm^3= \pi r^2 (12 \ cm)[/tex]
We want to find the radius, so we must isolate the variable. First, divide both sides by 12 centimeters.
[tex]1728 \pi \ cm^3/ 12 \ cm= \pi r^2 (12 \ cm)/12 \ cm[/tex]
[tex]144\pi \ cm^2= \pi r^2[/tex]
Divide both sides by pi.
[tex]144\pi \ cm^2 / \pi= \pi r^2/ \pi[/tex]
[tex]144 \ cm^2= r^2[/tex]
Take the square root of both sides.
[tex]\sqrt {144 \ cm^2}= \sqrt {r^2}[/tex]
[tex]12 \ cm=r[/tex]
The radius of the cylinder is 12 centimeters, but the question asks for the diameter. The diameter is twice the radius.
[tex]d=2r[/tex]
[tex]d= 2 (12 \ cm)[/tex]
[tex]d= 24 \ cm[/tex]
The diameter of the cylinder is 24 centimeters.