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

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

`\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.