Question

Shown below are perspective views of a hexagonal prism, a cube, and a cylinder, all having height 10 cm. If the objects are cut by straight planes to generate various cross-sections, which of the statements is/are TRUE?

• A. R can reveal curvilinear cross section; P and R can reveal a square cross section
• B. P, Q, and R can reveal rectangular cross sections; P and Q can reveal isosceles triangle
• C. P and Q can reveal regular hexagonal cross sections; R can reveal a square
• D. P and Q can reveal triangular cross sections

Hint:

For cross-section problems, visualize how each object could be cut at different angles. Circular and symmetrical objects like cylinders may reveal curvilinear sections.

Answer 1

The Correct Option is A, B, C

Step 1: The hexagonal prism (P) when cut can reveal various polygonal cross-sections, including hexagonal and rectangular sections. However, a square cross-section is not possible with this object unless cut in a very specific direction.
Step 2: The cube (Q) can easily reveal square cross-sections as it's a regular 3D object. It can also produce rectangular and other polygonal sections.
Step 3: The cylinder (R), due to its circular symmetry, can reveal curvilinear sections if cut at an angle to its axis. It can also reveal square cross-sections when cut perpendicular to its axis. Hence, both P and R can reveal square cross-sections under certain orientations of the cutting plane.
Step 4: After evaluating all possibilities, we conclude that the correct answers are (A), (B), and (C).