2 Answers

Bernhardt Scherer · Answer 1 · 2022-02-24T04:58:02+0000

Answer:

$\boxed {\boxed {\sf 24 \ centimeters}}}$

Explanation:

The volume of a cylinder is found using this formula:

$V= \pi r^2 h$

We know the height is 12 centimeters and the volume is 1728π cubic centimeters. We can substitute the values into the formula.

$1728 \pi \ cm^3= \pi r^2 (12 \ cm)$

We want to find the radius, so we must isolate the variable. First, divide both sides by 12 centimeters.

$1728 \pi \ cm^3/ 12 \ cm= \pi r^2 (12 \ cm)/12 \ cm$

$144\pi \ cm^2= \pi r^2$

Divide both sides by pi.

$144\pi \ cm^2 / \pi= \pi r^2/ \pi$

$144 \ cm^2= r^2$

Take the square root of both sides.

$\sqrt {144 \ cm^2}= \sqrt {r^2}$

$12 \ cm=r$

The radius of the cylinder is 12 centimeters, but the question asks for the diameter. The diameter is twice the radius.

d=2r

$d= 2 (12 \ cm)$

$d= 24 \ cm$

The diameter of the cylinder is 24 centimeters.

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