Area and volume SAT question

Math · Geometry and Trigonometry · Medium · Answer it here, explanation included.

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?

ExplanationShow

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.

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