Answer:
The radius of the cylinder is (1/2)x units
The area of the cylinder’s base is (1/4)πx2 square units
The height of the cylinder is 4x units
Step-by-step explanation:
The complete question is
A cylinder with a base diameter of x units has a volume of πx3 cubic units.
Which statements about the cylinder are true? Check all that apply.
(1) The radius of the cylinder is (1/2)x units.
(2) The radius of the cylinder is 2x units.
(3) The area of the cylinder’s base is (1/4)πx2 square units.
(4) The area of the cylinder’s base is (1/2)πx2 square units.
(5) The height of the cylinder is 2x units.
(6) The height of the cylinder is 4x units
we know that
The volume of the cylinder is equal to
[tex]V=\pi r^{2}h[/tex]
we have
[tex]r=\frac{x}{2}\ units[/tex] ----> the radius is half the diameter
[tex]V=\pi x^{3}\ units^3[/tex]
substitute the given values in the formula of volume
[tex]\pi x^3=\pi (\frac{x}{2})^{2}h[/tex]
solve for h
simplify
[tex]x=(\frac{1}{4})h[/tex]
[tex]h=4x\ units[/tex]
Verify each statement
(1) The radius of the cylinder is (1/2)x units
The statement is true
see the explanation
(2) The radius of the cylinder is 2x units.
The statement is false
Because, the radius of the cylinder is x/2 units
(3) The area of the cylinder’s base is (1/4)πx2 square units
The statement is true
Because, the area of the cylinder's base is equal to
[tex]A=\pi r^{2}[/tex]
[tex]r=\frac{x}{2}\ units[/tex]
substitute
[tex]A=\pi (\frac{x}{2})^{2}[/tex]
[tex]A=\frac{\pi x^2}{4}\ units^2[/tex]
(4) The area of the cylinder’s base is (1/2)πx2 square units.
The statement is false
Because, the area of the cylinder's base is equal to
[tex]A=\frac{\pi x^2}{4}\ units^2[/tex]
see the part (3)
(5) The height of the cylinder is 2x units.
The statement is false
Because, the height of the cylinder is 4x units (see the explanation)
(6) The height of the cylinder is 4x units
The statement is true
see the explanation
