Question

Which statements about the cylinder are true? Select two

Answer 1

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

$V=\pi r^{2}h$

we have

$r=\frac{x}{2}\ units$ ----> the radius is half the diameter

$V=\pi x^{3}\ units^3$

substitute the given values  in the formula of volume

$\pi x^3=\pi (\frac{x}{2})^{2}h$

solve for h

simplify

$x=(\frac{1}{4})h$

$h=4x\ units$

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

$A=\pi r^{2}$

$r=\frac{x}{2}\ units$

substitute

$A=\pi (\frac{x}{2})^{2}$

$A=\frac{\pi x^2}{4}\ units^2$

(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

$A=\frac{\pi x^2}{4}\ units^2$

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