Question

Two views of the same solid object are shown. Count the number of surfaces (planar or curved) the solid has.

Hint:

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.

Answer 1

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 \[ \boxed{18}\ \text{surfaces in total}. \]