Question

A cylinder with a base diameter of (x) units has a volume of (x³) cubic units. Which statements about the cylinder are true? Select two options.

A. The radius of the cylinder is (2x) units.

B. The area of the cylinder's base is (4pi x²) square units.

C. The area of the cylinder's base is ( pi x²) square units.

D. The height of the cylinder is (2x) units.

Answer 1

Of the given options, Statement C is correct: the area of the cylinder's base is (pi x^2) square units, and none of the other options accurately describe the radius or height of the cylinder.

Step-by-step explanation:

The question involves determining the truth of certain statements about a cylinder with a given base diameter (x) and volume (x³ cubic units), using the volume formula for a cylinder, V = πr²h, where V is the volume, r is the radius, and h is the height. Statement A suggests that the radius is (2x) units, which is not true since the diameter is given as x units, so the radius would be (x/2) units. Statement B implies that the base area is (4π x²) square units, which is incorrect because the correct base area for a cylinder is πr², making Statement C, which says the area of the cylinder's base is (π x²) square units, the correct one since the radius is half the diameter x. To find the height, we rearrange the volume formula: h = V/(πr²). Substituting the given values, we find h = x³/(π(x/2)²), which simplifies to h = 4x, meaning that Statement D is false. Therefore, the true statements are C and the correct height (not provided as an option).