Subject Test Math 2

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Subject Test Math 2

Question 12 of 28

The diameter and height of a right circular cylinder are equal. If the volume of the cylinder is $2$ , what is the height of the cylinder?

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$1.37$

Correct Answer:

Yes

$1.08$

Correct Answer:

No

$0.86$

Correct Answer:

No

$0.80$

Correct Answer:

No

$0.68$

Correct Answer:

No

View Correct Answer

The correct answer is A.

To determine the height of the cylinder, first express the diameter of the cylinder in terms of the height, and then express the height in terms of the volume of the cylinder.

The volume of a right circular cylinder is given by $V = π r^{2} h$ , where $r$ is the radius of the circular base of the cylinder and $h$ is the height of the cylinder. Since the diameter and height are equal, $h = 2 r$ . Thus $r = \frac{1}{2} h$ . Substitute the expression $\frac{1}{2} h$ for $r$ in the volume formula to eliminate $r$ : $V = π {(\frac{1}{2} h)}^{2} h = \frac{π}{4} h^{3}$ . Solving for $h$ gives $h = \sqrt[3]{\frac{4}{π} V}$ . Since the volume of the cylinder is $2$ , the height of the cylinder is $h = \sqrt[3]{\frac{8}{π}} \approx 1.37$ .