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A cylinder with a base diameter of x units has a volume of

cubic units

Which statements about the cylinder

options.

The radius of the cylinder is 2x units.

The area of the cylinder's base is ax? square units.

The area of the cylinder's base is nx square units.

The height of the cylinder is 2x units.

The height of the cylinder is 4x units.

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Corrected Question

A cylinder with a base diameter of x units has a volume of  [tex]\pi x^3[/tex] cubic units

Which statements about the cylinder are true? Check all that apply.

  • The radius of the cylinder is x units.
  • The radius of the cylinder is 2x units.
  • The area of the cylinder’s base is [tex]\dfrac{1}{4}\pi x^2[/tex] square units.
  • The area of the cylinder’s base is [tex]\dfrac{1}{2}\pi x^2[/tex] square units.
  • The height of the cylinder is 2x units.
  • The height of the cylinder is 4x units.

Answer:

  • The area of the cylinder’s base is [tex]\dfrac{1}{4}\pi x^2[/tex] square units.
  • The height of the cylinder is 4x units.

Step-by-step explanation:

If the Base Diameter = x

Therefore: Base radius [tex]=\dfrac{x}{2}$ units[/tex]

Area of the base [tex]=\pi r^2 =\pi (\dfrac{x}{2})^2 =\dfrac{\pi x^2}{4}$ square units[/tex]

Volume =Base Area X Height

[tex]\pi x^3 =\dfrac{\pi x^2}{4} X h\\$Height, h = \pi x^3 \div \dfrac{\pi x^2}{4}\\=\pi x^3 \times \dfrac{4}{\pi x^2}\\h=4x$ units[/tex]

Therefore:

  • The area of the cylinder’s base is [tex]\dfrac{1}{4}\pi x^2[/tex] square units.
  • The height of the cylinder is 4x units.

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