Acylinder 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 x units.
(2) the radius of the cylinder is 2x units.
(3) the area of the cylinder’s base is πx2 square units.
(4) the area of the cylinder’s base is πx2 square units.
(5) the height of the cylinder is 2x units.
(6) the height of the cylinder is 4x units.

The volume of the cylinder:
V = r² π h
We know that a base diameter: d = x
r = d / 2 = x / 2
π x³ = ( x/2 )² π h
π x³ = x²/4 π h  /:π
x³ = x²/4 h
h = x³ : x²/4= x³ · 4/x²
h = 4 x
As for the base: B = r² π = (x/2)² π = π x²/ 4

Correct statement is:
(6) The height of the cylinder is 4 x units.

The correct option is;

Yes, the line should be perpendicular to one of the rectangular faces

Step-by-step explanation:

A perpendicular cross-section of a triangular prism resting on a rectangular face will have a triangular cross-section section an either side of the line of the cross-section, therefore we have;

Given that the triangular prism is lying on one of the rectangular faces, the perpendicular cross-section will be represented by a line drawn along the slant height of the triangular prism, therefore the correct option is yes, the line should be perpendicular to one of the rectangular faces.