BITS U103 · Mid-sem tonight · graphics only

Engineering graphics: a crash course for the three mid-sem question types

This year's mid-sem graphics questions are three types: missing view, missing lines, and a sectional view (last year's Q7, Q8 and Q10). This page teaches each one from zero: the idea, the rule, a drawn construction, how to start, and the trap. About 75 minutes.

Start here

The graphics half of the paper is the most predictable part of this course. This year it is three types — last year's Q7, Q8 and Q10 — each drawn on the paper itself (you complete a drawing — nothing is computed). Each type has a fixed opening move, and marks come from correct construction and labelling as much as from the final shape. That is a learnable routine, not a talent.

Everything here is from your L4, L5, L6 and L12 slides. Watch the layout: last year's Q7 and Q8 drew the top view above the front view, not in the first-angle arrangement of the lecture examples. When views are already given, put the missing one where the given layout says it goes. To check which way round a view is, find one feature from the isometric (a step, slot or hole) and see which side of each view it lands on — the past-paper page shows how this proves Q7–Q8 are third angle, and this 4-minute narrated walkthrough animates it.

§	Type	Last year	Opening move
0	Exam toolkit	all	XY line, labels, line types
1	Missing view	Q7	mitre line at 45°, transfer depths
2	Missing lines	Q8	check every edge in every view
3	Section	Q10	remove the front part, hatch the cut

0 · The exam toolkit: where everything goes

Every graphics question is built on one picture. Imagine the object sitting in front of a vertical wall (the VP, vertical plane) and above the floor (the HP, horizontal plane). Look at it from the front and you see the front view (FV); look from above and you see the top view (TV). Then the floor is folded down flat, so the two views end up on one sheet, separated by the fold line: the XY line.

India uses first-angle projection (L4: the object sits in the first quadrant, between the observer and the plane). That fixes the layout:

FV above XY, TV below XY, on the same vertical projector.
The left view (LV), seen from the left, is drawn to the right of the FV.
Labels: a point A has a′ in the FV, a in the TV, a″ in the side view.
In the FV, the distance above XY is the height above HP. In the TV, the distance below XY is the distance in front of VP.

Point A, 20 mm above HP and 30 mm in front of VP. a′ and a share one vertical projector. The 30 mm depth turns the corner at the 45° mitre line and becomes the horizontal position of a″.

Line	How it looks	Means
Visible edge	thick, continuous	an edge you can see from that side
Hidden edge	thin, short dashes	an edge behind material (holes, slots seen from outside)
Centre line	thin chain (long–short)	axis of every hole, cylinder, symmetric part
Projector / construction	thin, light	lines that carry a point from one view to another — keep them, don't erase
Hatching	thin, 45°, evenly spaced	material cut by a section plane

How to start any graphics question: draw XY, write X and Y at its ends, and label every given point (a′, a, …) before drawing anything new. Points line up on vertical projectors between FV and TV — always.

Check yourself: point B is 35 mm above HP and 10 mm in front of VP. Where do b′, b and b″ go?

b′ 35 mm above XY; b 10 mm below XY on the same vertical line; b″ at height 35 mm, 10 mm to the right of the X₁Y₁ line (the depth, turned through the mitre).

Classic trap

Drawing the side view on the wrong side. In first angle the view from the left goes on the right. Most YouTube tutorials are American and use third angle (top view above, right view on the right) — a beautiful drawing in the wrong layout loses marks. More on this in Reading engineering drawings §3.

Time: 90 minutes for 12 five-mark questions is about 7 minutes per question. Graphics questions are pure construction — if one stalls, label what you have and move on.

1 · Missing view: two views given, draw the third

🎧 Watch (≈4 min): last year's Q7 missing view built feature by feature, narrated.

Each view shows two of the object's three sizes: the FV shows width and height, the TV shows width and depth, the side view shows depth and height. So a missing view never needs anything new: its heights come straight across from the FV, and its depths come from the TV, turned through the 45° mitre line.

Draw the X₁Y₁ line (a vertical line to the right of the FV) and the mitre line at 45° from where it meets XY.
Take one feature at a time (the base, then the step, then the hole). For each: carry its heights horizontally from the FV; carry its depths from the TV across to the mitre, then up.
Where the projectors cross, you have the feature's corners. Join them.
Decide visible or hidden for every edge: is there material between you and it, looking from that side? Holes and inside slots are hidden (dashed), with a centre line.

A block with a tall step at the back-left and a Ø12 vertical hole. Depths 20 and 40 travel from the TV to the mitre and up; heights 20 and 50 come across from the FV. The hole is a circle from above but a pair of dashed lines from the front and side.

Unpack this step: why a 45° line turns depth into horizontal distance

A 45° line rises one unit for every unit it goes across. So a projector that arrives at depth 30 below XY meets the mitre 30 to the right of X₁Y₁, then goes straight up. That is the same depth, rotated through a right angle: the floor folded flat.

If an isometric drawing is given too (last year's Q7 had one), use it only to understand the shape: which parts are tall, where the cut-outs are. Take every number from the given views or the isometric dimensions, never by measuring the isometric.

How to start: draw X₁Y₁ and the mitre line first, then transfer the outermost box (overall depth × overall height). Every feature then lives inside that box.

Check yourself: in the figure, why is the hole a solid circle in the TV but dashed lines in the FV and LV?

From above you look straight down the hole, so you see its edge as a circle. From the front and the side, the hole is inside the block: material is in front of it, so its two walls are hidden edges (dashed), with a chain centre line through the axis.

Classic traps

1) Measuring depth in the side view from the wrong end: in first angle, the side of the LV nearest the FV is the back of the object (the VP side), exactly as the top edge of the TV is the back. 2) Forgetting hidden lines and centre lines — they are part of the answer, not decoration.

The exam version: past paper Q7.

2 · Missing lines: complete three views

🎧 Watch (≈3 min): last year's Q8 missing lines, one feature at a time, narrated.

Here all three views are drawn, but some lines are left out. The rule that finds them: every edge of the object shows up in every view, as a visible line, a hidden line, or overlapping another line. And every line in one view must have a partner in the others (on the same projector).

The slides (L5) classify surfaces, which tells you what each one looks like in each view:

Surface	Is…	Shows as
Principal	parallel to one plane	true shape in one view, a line in the other two
Inclined	perpendicular to one plane, tilted to the others	a line in one view, a squashed shape in two
Skew (oblique)	tilted to all three	a squashed shape in all three
Curved	part of a cylinder	a circle/arc in one view, a rectangle in the others; draw a line only at its outer limit

A slot cut across the top, front to back. The FV shows it plainly. The lines most often missed (accent): the two slot edges running front-to-back in the TV, and the slot floor in the LV, which is hidden behind the left wall and so is dashed.

Go corner by corner in the view that shows the feature most clearly (usually the FV).
Drop a projector to the TV and across to the side view. Is there a line there? If not, decide: visible (thick) or hidden (dashed)?
For every hole: a circle in one view, two dashed lines plus a centre line in the other two.

How to start: pick one corner of a step or slot in the FV, follow its projector into the other views, and ask "where does this edge appear here?" Repeat for every corner.

Check yourself: a hole is drilled through a block from the front face to the back face. Which view shows a circle, and what do the other two show?

The FV shows the circle (you look straight into the hole). The TV and side view each show two dashed lines (the hole's walls) and a chain centre line along the axis.

Classic traps

1) A line where two surfaces are flush (same plane): there is no edge there, so no line. 2) A curved surface that blends smoothly into a flat one has no line at the tangent point; only its outer limit gets a line (L5: "the last visible part of a curved surface falls in a line view").

The exam version: past paper Q8.

3 · Sectional views

🎧 Watch (≈3 min): last year's Q10 sectional view, from the cutting plane to the hatching, narrated.

A section answers "what does the inside look like?" without a forest of dashed lines (L12). Imagine slicing the object along the cutting plane, throwing away the part between you and the cut, and drawing what remains.

Find the cutting-plane line in the given view: a chain line, thick at the ends, with arrows showing which way you look.
Remove the material between the observer and the plane.
Hatch every place the plane cuts through solid material: thin lines at 45°, evenly spaced, same direction for the whole part.
Don't hatch holes, slots or anywhere the plane passes through air. Draw the visible edges behind the cut (the back half of a hole shows as lines).
Hidden lines are normally left out of a sectional view; the section already shows the inside.

A block with a counterbored hole (Ø24 for 10 mm, then Ø12 through), cut along A-A through the hole's centre. The sectional FV hatches the two cut walls; the hole stays open, and the step inside it shows as a line.

Where the plane runs parallel to the VP, the sectional FV shows the true shape of the cut. (L12: parallel to HP → true shape in the sectional TV; inclined → an auxiliary view is needed.)

How to start: draw the outline of the remaining half first, then mark the regions the plane cuts through solid, and only then hatch them.

Check yourself: in a sectional view, does the hole get hatched? Do you draw its hidden lines?

No to both. The plane passes through air in the hole, so no hatching; and a sectional view replaces hidden lines with the cut itself.

Classic traps

1) Hatching the hole, or hatching the two halves of one part in opposite directions. 2) Forgetting the lines behind the cut: the far wall and the steps of a hole are visible edges.

The exam version: past paper Q10.

✏️ More practice at exam level: missing views & missing lines (9 problems) · sectional views (5 problems).

Tonight's plan (about 1½ hours)

0:00–0:50. This page, top to bottom. Do every "Check yourself" before opening it.
0:50–1:15. The past paper, Q7, Q8 and Q10, one at a time: read the question, write your opening move, then step through the drawing.
1:15–1:30. On paper, with the solutions covered: redraw Q7 (missing view) and Q10 (sectional view, hatched). Pencil, scale, compass.

Then stop and sleep. A rested hand draws cleaner projectors.

Exam-room checklist

Sharp pencils (one hard for construction, one soft for final lines), scale, compass, set squares, eraser.
XY line drawn and labelled X … Y on every question.
Layout: if views are already given, put the missing one where that layout says (last year's Q7–Q8 had the top view above). Starting fresh: first angle — FV above XY, TV below, left view on the right.
Every point labelled: a′ in FV, a in TV, a″ in side view.
Projectors thin and kept; never erase construction.
Final lines thick; hidden edges dashed; centre lines through every hole.
Sections: hatch only the cut solid, 45°, one direction; no hidden lines.
About 7 minutes a question; if stuck, label what you have and move on.