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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?

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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?

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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, $\\pi r^{2}$, 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 $45\\,\\pi=\\pi(r)^{2}(5)$. Dividing both sides of this equation by $5\\,\\pi$ yields $9=r^{2}$. Taking the square root of both sides yields $r=3$ or $r=-3$. 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 $45\\,\\pi=\\pi(r)^{2}(5)$ for $r^{2}$, not $r$, by dividing by $\\pi$ on both sides and then by subtracting, not dividing, 5 from both sides.

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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?

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4.5

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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?