Question

which statement must be true?

a cube can have a cross section that is a triangle.
a sphere can have a rectangle as a cross section.
a cone can have a cross section that is a square.
a cylinder can have a cross section that is a sphere.

Explanation:

Analyze the cross sections of each 3D shape

• A cube sliced by a plane passing through three adjacent corners yields an equilateral triangle.
• A sphere sliced by any plane always yields a circle.
• A cone sliced by a plane can yield circles, ellipses, parabolas, hyperbolas, or triangles, but never a square.
• A cylinder sliced by a plane yields 2D shapes (like circles, ellipses, or rectangles), never a 3D shape like a sphere.

Evaluate the given statements

• "A cube can have a cross section that is a triangle" is true.
• "A sphere can have a rectangle as a cross section" is false.
• "A cone can have a cross section that is a square" is false.
• "A cylinder can have a cross section that is a sphere" is false.

Answer:

• (A) A cube can have a cross section that is a triangle. (Correct answer)
• (B) A sphere can have a rectangle as a cross section.
• (C) A cone can have a cross section that is a square.
• (D) A cylinder can have a cross section that is a sphere.