Work through these eight original questions in order, writing your working first. They cover the four lessons in surface development concepts.
Questions
1. How many faces does a closed triangular prism have, and what shapes are they?
Answer
Five: two triangles for the ends and three rectangles for the sides.
2. A cylinder has diameter 10 mm and height 25 mm. Give the size of the rolled-out rectangle. Use π ≈ 3.142.
Answer
Height 25 mm. Length is the circumference, π × 10 = 31.42, about 31.4 mm.
3. A closed box measures 50 mm by 20 mm by 15 mm. List the six faces by size.
Answer
Two of 50 × 20, two of 50 × 15 and two of 20 × 15. Check: each pair appears on opposite sides of the box.
4. In a cross-shaped net of an open box with height 12 mm, how many seam edges of 12 mm are shown, and how many pairs do they form?
Answer
Eight edges of 12 mm, forming four pairs, one for each vertical corner.
5. A net for a cube of edge 30 mm has six squares, and one square has sides 28 mm. Which check fails, and how do you repair it?
Answer
The count passes, but the length match fails: a 28 mm edge cannot meet a 30 mm edge. Redraw that square at 30 mm by 30 mm.
6. A cylinder has diameter 18 mm and height 40 mm. A student draws a rectangle 40 mm high and 54 mm long. Is it compatible with the end circles (π ≈ 3.142)?
Answer
The circumference is π × 18 = 56.56, about 56.6 mm. The rectangle is 2.6 mm short, so it does not wrap the circle. The long edge should be about 56.6 mm.
7. An open box has a base 30 mm by 20 mm and height 10 mm. Find the total seam length of a cross-shaped net.
Answer
The seams are the four vertical corners, each 10 mm: 4 × 10 = 40 mm.
8. For the box in question 7, compare a strip layout in which the four sides form one row and the base is attached to a 30 mm side. Which has the shorter seam, and by how much?
Answer
Strip seam: one vertical corner, 10 mm, plus three base edges: 20 + 30 + 20 = 70 mm, so 80 mm in total. The cross has a 40 mm seam, which is shorter by 40 mm.
If you got these wrong
- Questions 1, 2 and 3: reread connecting a solid to its development.
- Question 4: reread tracing corresponding edges.
- Questions 5 and 6: reread checking a development for faults.
- Questions 7 and 8: reread explaining a development choice.
Next, combine all the skills in integrated drawing practice.
If you want a teacher to set fresh questions and check your reasoning, see online one-to-one Engineering Drawing tuition.