BITS U103 · Self-marking practice
Rebuild drills
Eight parts, rising in difficulty. Model each from the drawing, then let Fusion mark your work — every drill states the exact volume the finished part must have. Match it and you know you're right, to the cubic millimetre.
Fusion computes the volume of any solid you build. So you don't need someone to check your work: if your volume matches the answer key, your model is correct. If it doesn't, the size of the gap usually tells you what you missed — a whole missing hole, or a wall 1 mm too thick.
To read your volume: Inspect → Physical Properties, or right-click the body in the Browser and choose Properties. Volume doesn't depend on material, so ignore the density and mass figures — any material gives the same volume.
One drill per sitting, roughly one a day. Read the drawing, decide the feature tree before touching the mouse, then build it. Every sketch fully constrained, no exceptions.
Each drill hides two things: the answer key (volume) and the method (a suggested feature tree). Open the method only after you've either finished or genuinely stuck — reading it first turns a drill into a tutorial, and tutorials don't build skill.
All dimensions are in millimetres. Drawings are in first angle.
Drill 1 — Plate
A rectangular plate
- 80 × 50, thickness 10.
- One corner on the origin.
Answer key — volume
40 000 mm³ (40 cm³)
If you're out by a factor of 1000, check your document units — you may be modelling in centimetres.
See the method
- Sketch on the XY plane: 2-point rectangle R, one corner coincident with the origin.
- Dimension D 80 and 50. Confirm the sketch goes black.
- Extrude E 10. Done — 80 × 50 × 10 = 40 000.
Drill 2 — Plate with holes
The same plate, drilled
- Plate 80 × 50 × 10, as drill 1.
- Four holes ⌀8, right through, each centred 15 from both nearest edges.
Answer key — volume
37 989.38 mm³ (37.99 cm³)
Off by about 502.7? One hole is missing. Off by 40 000 − yours = a round 2010.6? All four holes failed to cut — check the extrude operation was set to Cut, not New Body.
See the method
- Build drill 1's plate.
- Sketch one circle on the top face, ⌀8, positioned 15 and 15 from the corner.
- Extrude it, operation Cut, extent All.
- Rectangular pattern the cut feature: 2 × 2, spacing 50 and 20. Modelling four separate circles also works but is exactly the habit the features lesson warns about.
Volume: 40 000 − 4 × π × 4² × 10 = 40 000 − 640π.
Drill 3 — L-bracket
An L-section bracket
- L cross-section: 60 wide, 58 tall overall, both legs 8 thick.
- Extruded 80 deep.
Answer key — volume
70 400 mm³ (70.40 cm³)
Got 75 520? You built the two legs as separate boxes and double-counted the 8 × 8 × 80 corner where they overlap (5 120 mm³) — a neat illustration of why one profile beats two boxes.
See the method
- Sketch the L profile on the XZ plane, anchored at the origin — six lines, all horizontal or vertical.
- Constrain: horizontal/vertical on every line, then dimension 60, 58, and 8 twice. It should reach zero DOF.
- Extrude 80. One feature, one body.
Volume: L area = 60 × 8 + 50 × 8 = 880 mm²; 880 × 80 = 70 400.
Drill 4 — Stepped block
A block with a rebate
- Overall 100 long × 60 deep × 45 tall.
- A step: the upper portion is 30 deep and stands 25 above the 20-thick base, running the full 100 length.
Answer key — volume
195 000 mm³ (195 cm³)
See the method
Two valid trees — both give the same solid, and it's worth building both to feel the difference:
- One profile: sketch the stepped L outline on the YZ plane, extrude 100. One feature.
- Cut: extrude a plain 100 × 60 × 45 block, then extrude-cut the 100 × 30 × 25 notch from the top.
Volume either way: 60 × 20 × 100 + 30 × 25 × 100 = 120 000 + 75 000 = 195 000. (Or 270 000 − 75 000 if you think of it as a cut.)
Drill 5 — Stepped shaft
A two-diameter shaft
- ⌀40 for 30 long, then ⌀25 for 50 long. Total length 80.
- Build it by revolving the half-profile shown — not by extruding two circles.
Answer key — volume
62 242.80 mm³ (62.24 cm³)
Note the profile drawn is the half section, measured from the axis: radii 20 and 12.5. Sketching it with the full diameters as heights is the standard first mistake and gives four times the volume.
See the method
- Sketch the profile on the XZ plane with its flat bottom edge on the X axis — that edge becomes the axis of revolution.
- Six lines, fully constrained: lengths 30 and 50, heights 20 and 12.5.
- Revolve, axis = the X axis, angle 360°.
Volume: π × 20² × 30 + π × 12.5² × 50 = π(12 000 + 7 812.5) = 19 812.5π.
Drill 6 — Shelled box
An open-topped box
- External size 80 × 60 × 40.
- Walls and floor 3 thick; top face open.
Answer key — volume
44 148 mm³ (44.15 cm³)
Got 56 136? You shelled the block without removing any face, so it came out sealed — a closed box with a 3 mm lid as well, which is more material, not less. Re-run Shell and select the top face as the one to remove. A much larger number again means the shell went outwards; check the direction setting.
See the method
- Sketch 80 × 60 on the XY plane, extrude 40 → a solid block.
- Shell (Modify menu), thickness 3, and select the top face as the face to remove.
Volume: 80 × 60 × 40 − 74 × 54 × 37 = 192 000 − 147 852. The cavity is 6 mm narrower in each horizontal direction (a wall on each side) but only 3 mm shorter vertically (a floor, no lid) — that asymmetry is the whole check.
Drill 7 — Filleted plate
Rounded plate with a hole pattern
- Plate 100 × 70 × 12.
- All four corners filleted R15.
- Six holes ⌀10 in a 3 × 2 grid: centres at 25, 50, 75 along the length and at 20, 50 across the width.
Answer key — volume
76 027.43 mm³ (76.03 cm³)
See the method
- Sketch 100 × 70 anchored at the origin, extrude 12.
- Fillet the four vertical corner edges, R15, all four selected in one feature.
- One hole ⌀10 through, then a rectangular pattern 3 × 2 with spacings 25 and 30.
Volume: each R15 corner removes 15² − π·15²/4 = 225(1 − π/4) ≈ 48.29 mm²; four corners ≈ 193.14 mm². Six holes remove 6 × 25π ≈ 471.24 mm². Net area ≈ 6 335.62 mm², × 12 thickness.
Drill 8 — The full bracket
L-bracket with rib and holes
- Start from drill 3's bracket: L section 60 × 58, legs 8 thick, extruded 80.
- Rib: a right triangle in the inner corner, legs 30 up the wall and 30 along the base, 10 thick, centred across the 80 depth (so it occupies 35–45).
- Holes, all ⌀9 and all right through their leg: four in the base at 25 and 50 along the length, 15 and 65 across the depth; two in the upright at 45 up from the base, 20 and 60 across the depth.
Answer key — volume
71 846.37 mm³ (71.85 cm³)
Sanity checkpoints as you go: after the L extrude, 70 400. After adding the rib, 74 900. After the six holes, the figure above.
See the method
- Build drill 3's L-bracket.
- Rib: sketch the triangle on the YZ plane through the middle of the part (or on an offset plane at 35), extrude symmetric 10 total, operation Join. Symmetric extrusion is what centres it without arithmetic.
- Holes: Hole tool H, ⌀9, extent All. Place one in the base, pattern it 2 × 2; place the two upright holes separately.
- Check the rib and holes don't intersect — the rib sits at depth 35–45, the base holes at 15 and 65.
Volume: 70 400 + (½ × 30 × 30 × 10) − 6 × π × 4.5² × 8 = 70 400 + 4 500 − 972π.
When your number doesn't match
A mismatch is information, not failure. Work through it in this order:
| Symptom | Usual cause |
|---|---|
| Out by a factor of 1000 or 1 000 000 | Units. Check Document Settings is mm, and check whether the panel is reporting cm³. |
| Out by exactly one hole's worth | A cut that didn't go all the way through, or a pattern that made 3 instead of 4. |
| Too big, by a neat rectangular amount | An extrude set to New Body instead of Cut — you added material where you meant to remove it. |
| Too big, by a small corner-shaped amount | Two features overlapping and double-counted, or a missing fillet. |
| Slightly off, no obvious pattern | A blue sketch. An under-constrained profile settled at not-quite the dimensions you thought. Go back and constrain it fully. |
| Fusion reports several bodies | Your features made separate lumps instead of joining. Check the operation setting on each; Physical Properties measures the selected body only. |
Matching the volume doesn't guarantee the model is good. A part built with fixed sketches, no constraints and twelve separate features can hit the number exactly and still be unusable the moment a dimension changes.
So use the volume as the correctness check it is, and judge the quality separately: is every sketch black? Is the tree short? Could you change the overall length in one place? A drill isn't really finished until both answers are yes.
The tutorial sheets are pitched a level above these. When drill 8 feels routine, read From drawing to model (lesson 5) and move on to the level-2 drills — four machine parts climbing to full tutorial-sheet difficulty, with staged volume checkpoints.