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Subjects · Leaving Cert Design & Communication Graphics (DCG)

Leaving Cert Design & Communication Graphics (DCG): Sections of solids

How often Sections of solids comes up on the Design & Communication Graphics papers, every year it was asked, and questions to try.

HL Asked on 3 of the last 9 Higher Level papers, most recently in 2024.

OL Asked on 1 of the last 9 Ordinary Level papers, most recently in 2024.

Sections of solids, Higher Level(7 marks)

Quick ones on Sections of solids.

(a)A plane cuts a right cylinder at an angle to its axis, through every generator. What is the true shape of the section?
  1. A circle
  2. An ellipse
  3. A parabola
(b)What is the true shape of any plane section of a sphere?
  1. It depends on the angle of the cut
  2. An ellipse
  3. A circle
(c)A sphere of radius 50 mm is cut by a plane 30 mm from its centre. What is the radius of the section?
  1. 40 mm
  2. ≈58.3 mm
  3. 20 mm
Show the answers

(a) An ellipse

(b) A circle

(c) 40 mm

Your turn: Higher Level questions on Sections of solids.

Higher Level

Asked on 3 of the last 9 Higher Level papers, most recently in 2024.

Every paper, year by year

YearWhere it came up
2025Not asked
2024B1
2023Not asked
2022Not asked
2021Not asked
2019Not asked
2018Not asked
2017B1
2016B2, B3

Links open the State Examinations Commission’s paper for that year.

More Sections of solids questions

Sections of solids, 3 marks

A cube is cut by a plane through the three corners next to one corner. What is the true shape of the section?

  1. A right-angled triangle
  2. A square
  3. An equilateral triangle
Show the answer

An equilateral triangle

Each side of the section is a face diagonal of the cube, a√2 long, so all three sides are equal. The plane is square to the space diagonal from the cut-off corner.

Sections of solids, 3 marks

A cube is cut by a plane containing two opposite edges that do not share a face. What is the section?

  1. A regular hexagon: six equal sides
  2. A rectangle: edge × face diagonal
  3. A square: face diagonal × face diagonal
Show the answer

A rectangle: edge × face diagonal

The plane holds two parallel edges (length a) and crosses the cube along two face diagonals (a√2), so the section is a rectangle about 1.41 times as long as it is wide.

Ordinary Level

Asked on 1 of the last 9 Ordinary Level papers, most recently in 2024.

Every paper, year by year

YearWhere it came up
2025Not asked
2024A3
2023Not asked
2022Not asked
2021Not asked
2019Not asked
2018Not asked
2017Not asked
2016Not asked

Links open the State Examinations Commission’s paper for that year.

More Sections of solids questions

Sections of solids, 2 marks

What does the true shape of a section show?

  1. The outline of the solid before it has been cut
  2. Only the hidden edges behind the cut
  3. The cut surface at its real size and shape
Show the answer

The cut surface at its real size and shape

An inclined cutting plane looks like a line in one view and distorted in the other. A view parallel to the plane shows the cut face true size.

Sections of solids, 3 marks

A right cone is cut by a vertical plane through its apex. What is the section?

  1. A parabola
  2. A triangle
  3. A circle
Show the answer

A triangle

A plane through the apex contains straight generators, so the cut is bounded by straight lines: a triangle.

Sections of solids, 3 marks

A right cylinder is cut by a plane tilted to its axis, missing both ends. What is the true shape of the section?

  1. An ellipse
  2. A circle
  3. A parabola
Show the answer

An ellipse

A tilted cut across all the generators of a cylinder gives an ellipse. Its minor axis equals the cylinder's diameter.

Other Design & Communication Graphics (DCG) topics

All of Leaving Cert Design & Communication Graphics (DCG)