Respuesta :
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.
