Question:
Two views of the same solid object are shown. Count the number of surfaces (planar or curved) the solid has. 
Two views of the same solid object are shown. Count the number of surfaces (planar or curved) the solid has.
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From orthographic views, partition the object into feature groups (outer block, recesses, protrusions, curved cuts). Count faces per group and add; curved patches count as one surface each.
Updated On: Aug 28, 2025
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Solution and Explanation
Step 1: Start from the outer block.
Visible from the orthographic views, the outer block contributes five exterior rectangular faces (front–lower, back, left, right, bottom). \(⇒ 5\) faces so far.
Step 2: Add the pyramid.
The top pyramid contributes its four triangular faces (the top horizontal face under it is removed). \(⇒ +4 = 9\).
Step 3: Count the right-hand rectangular notch.
That recess has three interior faces: two vertical side walls and one horizontal floor. \(⇒ +3 = 12\).
Step 4: Count the front scoop.
The concave semi-cylindrical scoop contributes one curved cylindrical surface, plus a vertical back wall closing it. \(⇒ +2 = 14\).
Step 5: Remaining top flats/ledges.
Around the scoop and toward the right step there are four distinct planar terraces/ledges (as read from the two views). \(⇒ +4 = 18\).
Therefore the solid has \[ \boxed{18}\ \text{surfaces in total}. \]
Visible from the orthographic views, the outer block contributes five exterior rectangular faces (front–lower, back, left, right, bottom). \(⇒ 5\) faces so far.
Step 2: Add the pyramid.
The top pyramid contributes its four triangular faces (the top horizontal face under it is removed). \(⇒ +4 = 9\).
Step 3: Count the right-hand rectangular notch.
That recess has three interior faces: two vertical side walls and one horizontal floor. \(⇒ +3 = 12\).
Step 4: Count the front scoop.
The concave semi-cylindrical scoop contributes one curved cylindrical surface, plus a vertical back wall closing it. \(⇒ +2 = 14\).
Step 5: Remaining top flats/ledges.
Around the scoop and toward the right step there are four distinct planar terraces/ledges (as read from the two views). \(⇒ +4 = 18\).
Therefore the solid has \[ \boxed{18}\ \text{surfaces in total}. \]
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