How the problems are made
Each solid stands on its base on the HP and is cut by a plane perpendicular to the VP through a point of its axis, all from whole-number data as a question paper gives it. The key is the full construction, drawn full size: front view, sectional top view, the true shape by an auxiliary view, and the development of the lower part, with the cut points carried to a true-length edge first. Printed at 100%, you can lay your sheet over it.
The five levels
- Frustums: a pyramid or cone cut parallel to its base.
- Prisms cut by an inclined plane, sometimes through the top or the base.
- Pyramids cut by an inclined plane.
- Cylinders: an elliptical section and a curved development.
- Cones: an elliptical section and a sector development.
An example from set ABCDEF
A triangular pyramid, base 35 mm side and axis 65 mm long, is cut at 40° to the HP through the point of its axis 20 mm above the base. Its slant edges are 68.1 mm true length (√(20.21² + 65²)). The true shape is a triangle with a longest side of 33.5 mm. On the development the slant edges left on the lower part run from 7.2 mm to 29.6 mm, measured on the true-length edge. Open set ABCDEF
Questions
What is the true shape of a section?
The real shape of the cut face, seen square to the section plane. A plane inclined to the HP shows the section foreshortened in the top view, so it is projected on an auxiliary plane parallel to the section plane to show its true size.
How do you draw the true shape of a section?
Through each point where the VT cuts an edge, draw a line square to the VT. Draw X₁Y₁ parallel to the VT and, on each line, set off the point's distance from XY in the top view (the keys use a centre line instead, with distances from the top view's centre line: the same shape). Join the points and hatch.
What is the difference between parallel-line and radial-line development?
Parallel-line development is for prisms and cylinders, whose edges are parallel: the surface unrolls into a strip as long as the perimeter or πD. Radial-line development is for pyramids and cones, whose edges meet at the apex: the surface unrolls into a fan about the apex, with the true slant length as radius.
How do you find the sector angle of a cone's development?
Sector angle = 360 × r ÷ l, where r is the base radius and l the slant height, √(r² + h²). A cone of 50 mm diameter and 60 mm height has l = 65 mm, so the angle is 360 × 25 ÷ 65 = 138.5°.
Why carry a cut point across to the true-length edge?
A slant edge inclined to the VP looks shorter in the front view, so a length measured along it is wrong. Draw a horizontal from the cut point to an edge that shows its true length (the outline of a cone, or an edge swung parallel to the VP) and measure there.
Why is the section of a cylinder an ellipse?
An inclined plane meets each generator at a different height. Across the plane the section is as wide as the cylinder, D; along the VT it is D ÷ cos α. Those are the minor and major axes of the ellipse.
How do I use this with a class?
Share with class sends a link to the same problems. To stop copying, print a class set: each student gets a different set, and the full-size keys follow, labelled by copy number.
Methods checked 26 October 2026: NPTEL Engineering Drawing, lecture 32 (sections) and lecture 36 (developments); Rajagiri (KTU) Engineering Graphics notes on sections and developments (PDFs); syllabi of KTU and Mumbai FEC204 (PDFs).