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Test
Math
Domain
Geometry and Trigonometry
Skill
Area and volume
Difficulty
Medium
ID: f67e4efc
Modded SAT Question Bank by Abdullah Mallik

A right circular cylinder has a volume of 45 pi. If the height of the cylinder is 5, what is the radius of the cylinder?

  1. 3

  2. 4.5

  3. 9

  4. 40

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Correct Answer: A
Rationale

Choice A is correct. The volume of a right circular cylinder with a radius of r is the product of the area of the base, pi, r squared, and the height, h. The volume of the right circular cylinder described is 45 pi and its height is 5. If the radius is r, it follows that 45 pi equals, pi times, r, squared, times 5. Dividing both sides of this equation by 5 pi yields 9 equals r squared. Taking the square root of both sides yields r equals 3 or r equals negative 3. Since r represents the radius, the value must be positive. Therefore, the radius is 3.

Choice B is incorrect and may result from finding that the square of the radius is 9, but then from dividing 9 by 2, rather than taking the square root of 9. Choice C is incorrect. This represents the square of the radius. Choice D is incorrect and may result from solving the equation 45 pi equals, pi times, r, squared, times 5 for r squared, not r, by dividing by pi on both sides and then by subtracting, not dividing, 5 from both sides.

 

Question Difficulty: Medium
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