What is the volume of the right circular cylinder X ?

Target question: What is the volume of the right circular cylinder X ?
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Aside: A right circular cylinder is a cylinder whose bases are aligned directly above the other.
So, the cylinder on the left (below) is a right cylinder, and the one on the right is an oblique cylinder

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Key property: Volume of cylinder \(= \pi r^2 h\)

Statement 1: The height of X is 20
Since we still don't know the radius of the cylinder, statement 1 is NOT SUFFICIENT

Statement 2: The base of X has area 25π.
Area of a circle \(= \pi r^2\)
So statement 2 is telling us that: \( \pi r^2 = 25 \pi\)
Since we still don't know the height of the cylinder, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that \(h = 20\)
Statement 2 tells us that \( \pi r^2 = 25 \pi\)
So the volume of the cylinder \(= \pi r^2 h = (25 \pi)(20) = 500 \pi\)
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent