Question

A cylinder with a height of 12 cm has a volume of 1728 pi cm^ 3 What is the diameter of the cylinder?

Answer 1

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 2

Answer:

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

Step-by-step 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.