a cylinder with a base diameter of x units has a volume of $pi x^3$ cubic units.\nwhich statements about the…

a cylinder with a base diameter of x units has a volume of $pi x^3$ cubic units.\nwhich statements about the cylinder are true? select two options.\n$square$ the radius of the cylinder is 2x units.\n$square$ the area of the cylinders base is $\frac{1}{4}pi x^2$ square units.\n$square$ the area of the cylinders base is $\frac{1}{2}pi x^2$ square units.\n$square$ the height of the cylinder is 2x units.\n$square$ the height of the cylinder is 4x units.

a cylinder with a base diameter of x units has a volume of $pi x^3$ cubic units.\nwhich statements about the cylinder are true? select two options.\n$square$ the radius of the cylinder is 2x units.\n$square$ the area of the cylinders base is $\frac{1}{4}pi x^2$ square units.\n$square$ the area of the cylinders base is $\frac{1}{2}pi x^2$ square units.\n$square$ the height of the cylinder is 2x units.\n$square$ the height of the cylinder is 4x units.

Answer

Explanation:

Step1: Find the cylinder's radius

Radius $r = \frac{\text{diameter}}{2} = \frac{x}{2}$ units

Step2: Calculate base area

Base area $A = \pi r^2 = \pi \left(\frac{x}{2}\right)^2 = \frac{1}{4}\pi x^2$ square units

Step3: Solve for cylinder height

Volume formula: $V = A \times h$. Substitute $V=\pi x^3$, $A=\frac{1}{4}\pi x^2$: $\pi x^3 = \frac{1}{4}\pi x^2 \times h$ Divide both sides by $\pi x^2$: $h = 4x$ units

Step4: Verify each statement

  1. Radius = $2x$: False (radius is $\frac{x}{2}$)
  2. Base area = $\frac{1}{4}\pi x^2$: True
  3. Base area = $\frac{1}{2}\pi x^2$: False
  4. Height = $2x$: False
  5. Height = $4x$: True

Answer:

B. The area of the cylinder's base is $\frac{1}{4}\pi x^2$ square units. E. The height of the cylinder is 4x units.