Question

The figure shows perspective views of the same solid object. Which option shows the count of the total number of surfaces?

• A. 15
• B. 20
• C. 19
• D. 17

Hint:

When counting surfaces on a complex 3D object, break it down into simpler geometric components or categorized surfaces (e.g., top, bottom, sides, features). Mentally "paint" each surface to keep track of what you've counted.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
This problem requires careful 3D visualization and systematic counting of all the distinct faces or surfaces of a complex object, using multiple views to understand its complete geometry.
Step 2: Detailed Explanation:
To accurately count the surfaces, we can methodically identify each one, ensuring none are missed or double-counted. Let's categorize the surfaces by their orientation and location:

Bottom Surface: There is one flat surface on which the object rests. (1 surface)
Top-Facing Surfaces: There are three distinct surfaces facing upwards: the main top surface, the top of the raised rectangular block, and the flat top of the cylindrical part. (3 surfaces)
Groove Surfaces: The wavy groove cut into the top consists of three surfaces: the curved bottom of the groove and its two vertical side walls. (3 surfaces)
Cylindrical Feature Surfaces: The cylinder has its top face (already counted), its curved side, the flat underside of its overhang, and the vertical face on the main body that the overhang covers. (3 surfaces)
Raised Block Surfaces: The raised block has its top face (already counted), its front-facing vertical surface, and its right-facing vertical surface. (2 surfaces)
Main Body Side Surfaces: Let's count the remaining vertical and side faces of the main L-shaped body.

The front face of the L's vertical leg. (1 surface)
The back face of the L's vertical leg. (1 surface)
The left side face of the object. (1 surface)
The right side face of the object (below the raised block). (1 surface)
The inner vertical face of the L-corner. (1 surface)

Let's sum up the count from this breakdown: \[ 1 (\text{Bottom}) + 3 (\text{Top}) + 3 (\text{Groove}) + 3 (\text{Cylinder part}) + 2 (\text{Block part}) + 5 (\text{Main Body sides}) = 17 \text{ surfaces} \]
Step 3: Final Answer:
By systematically identifying and counting each distinct surface of the object, the total count is 17.