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Subject Test Math 2

Question 12 of 28

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SAT Subject Test

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

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 equals pi r to the power of 2 end exponent 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 equals 2 r. Thus r equals fraction numerator 1 over denominator 2 end fraction h. Substitute the expression fraction numerator 1 over denominator 2 end fraction h for r in the volume formula to eliminate r: V equals pi left parenthesis fraction numerator 1 over denominator 2 end fraction h right parenthesis to the power of 2 end exponent h equals fraction numerator pi over denominator 4 end fraction h to the power of 3 end exponent. Solving for h gives h equals root index 3 of fraction numerator 4 over denominator pi end fraction V end root. Since the volume of the cylinder is 2, the height of the cylinder is h equals root index 3 of fraction numerator 8 over denominator pi end fraction end root almost equal to 1.37.

Question Difficulty: 
medium