the volume of a cylinder is 54 Pi centimeters to the third if the radius is 3 cm what is the height of the cylinder

1 answer:

6 0

The height of the cylinder is 6 cm.

If the volume of the cylinder is 54π cm³, and we know the radius, we can use the formula for the volume of a cylinder to figure out the length of the height.

V = πr²h

Substitute

54π = 9h<span>π
</span>
Divide each side by <span>π
54 = 9h

Get h by itself

h = 6, which means that the height of the cylinder is 6 cm. </span>

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<h2>Answer:</h2>

$\boxed{(5(-\sqrt{2}+\sqrt{6}),5(\sqrt{2}+\sqrt{6}))}$

<h2>Step-by-step explanation:</h2>

The origin of the coordinate system is the center of the circle. So we have an angle that measures $5\pi/12=75^{\circ}$ . so the x-coordinate and y-coordinate can be found, by using trigonometry as follows:

$x=20cos(5\pi/12)=5\sqrt{6}-5\sqrt{2} \\ \\ Arranging:\\ \\x=5(-\sqrt{2}+\sqrt{6}) \\ \\y=20sin(5\pi/12)=5\sqrt(6)+5\sqrt{2} \\ \\ Arranging:\\ \\y=5(\sqrt{2}+\sqrt{6})$