Question

Count the no of sloping surfaces.

• A. 6
• B. 8
• C. 4
• D. None of the above

Hint:

When asked to count specific types of surfaces in a complex 3D visual: 1. \textbf{Deconstruct the Object:} Break down the complex shape into simpler, recognizable geometric solids (e.g., prisms, pyramids, cones, cylinders). 2. \textbf{Define the Surface Type:} Clearly understand what criteria define the "sloping surface" (i.e., neither horizontal nor vertical). 3. \textbf{Systematic Scan per Component:} Go through each identified component and systematically inspect all its faces (top, bottom, and sides) against the definition of a sloping surface. This prevents miscounting or overlooking surfaces.

Answer 1

The Correct Option is C

Step 1: Understand the Definition of "Sloping Surfaces"
A "sloping surface" refers to a face of a three-dimensional object that is inclined at an angle, meaning it is neither perfectly horizontal (flat, parallel to the ground) nor perfectly vertical (straight up and down, perpendicular to the ground). Our task is to identify and count only these inclined faces in the given illustration. Step 2: Analyze the Structure of the Object
The object depicted in the image is a composite 3D shape, appearing to be made of two distinct geometric components stacked together:
1. Bottom Part: This is a rectangular block or prism (a cuboid).
2. Top Part: This is a truncated pyramid (also known as a frustum of a pyramid), which means it's a pyramid with its top cut off, leaving a smaller flat top surface parallel to its base. Step 3: Systematically Count Sloping Surfaces for Each Part
For the Bottom Part (Rectangular Prism):
Top surface: This face is flat and horizontal. (Not sloping) Bottom surface: This face is flat and horizontal (resting on the ground). (Not sloping)
Side surfaces (4 faces: front, back, left, right): These faces are flat and perfectly vertical. (Not sloping)
Therefore, the bottom part has 0 sloping surfaces. For the Top Part (Truncated Pyramid / Frustum):
Top surface: This face is flat and horizontal (the smaller top square/rectangle). (Not sloping)
Bottom surface: This face is flat and horizontal (its base resting on the bottom part). (Not sloping)
Side surfaces (4 faces): These are the four trapezoidal faces that connect the smaller top square/rectangle to the larger base (which sits on the bottom tier). By their very nature, these four faces are inclined or sloped.
Therefore, the top part has 4 sloping surfaces. Step 4: Calculate the Total Number of Sloping Surfaces
To find the total, we sum the sloping surfaces from both parts:
Total sloping surfaces = (Sloping surfaces in bottom part) + (Sloping surfaces in top part)
Total sloping surfaces = 0 + 4 = 4. This total count of 4 perfectly matches option C.