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Subjects · Leaving Cert Design & Communication Graphics (DCG)

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

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

HL Asked on 6 of the last 9 Higher Level papers, most recently in 2025. most years

OL Asked on 9 of the last 9 Ordinary Level papers, most recently in 2025. banker

Interpenetration of solids, Higher Level(8 marks)

Quick ones on Interpenetration of solids.

(a)What is the usual method for finding the curve of interpenetration of two curved solids?
  1. Rotation of the solids
  2. Auxiliary cutting planes
  3. Development of both surfaces
(b)Where are the points at which a curve of interpenetration changes from visible to hidden?
  1. On the base of the solids
  2. On the axis of the larger solid
  3. On the contour (outline) generators
(c)Two cylinders of equal diameter have axes meeting at 90°. In the view parallel to both axes, the intersection appears as what?
  1. Two straight lines crossing
  2. Two hyperbolas crossing
  3. Two circular arcs meeting
Show the answers

(a) Auxiliary cutting planes

(b) On the contour (outline) generators

(c) Two straight lines crossing

Your turn: Higher Level questions on Interpenetration of solids.

Higher Level

Asked on 6 of the last 9 Higher Level papers, most recently in 2025. most years

Every paper, year by year

YearWhere it came up
2025A4
2024Not asked
2023B1
2022A3
2021A4
2019A3
2018Not asked
2017Not asked
2016B3

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

More Interpenetration of solids questions

Interpenetration of solids, 3 marks

Two prisms interpenetrate. How are the corners of the line of interpenetration found?

  1. Where the bases of the two prisms cross in plan
  2. By drawing auxiliary circles round each of the prisms
  3. Where each prism's edges pierce the other's faces
Show the answer

Where each prism's edges pierce the other's faces

Where an edge of one prism passes through a face of the other the line of interpenetration turns a corner. Find those piercing points in the views and join them in order.

Interpenetration of solids, 3 marks

Two solids of revolution have intersecting axes. In the cutting-sphere method, where are the spheres centred?

  1. On the XY line
  2. At the point where the axes meet
  3. At the centre of the larger base
Show the answer

At the point where the axes meet

A sphere centred on an axis cuts that solid in circles. Centred where both axes meet, it cuts both solids in circles, which show as straight lines in the view parallel to both axes.

Interpenetration of solids, 3 marks

A small cylinder meets a larger one, axes intersecting at 90°. How does the curve look in the view parallel to both axes?

  1. Curved, bowing towards the larger's axis
  2. Two straight lines crossing at the axis
  3. A full circle, the size of the small one
Show the answer

Curved, bowing towards the larger's axis

The small cylinder's front generators strike the large surface lower than its side ones, so the curve bows into the large cylinder. Only equal diameters give straight lines.

Ordinary Level

Asked on 9 of the last 9 Ordinary Level papers, most recently in 2025. banker

Every paper, year by year

YearWhere it came up
2025B1
2024B3
2023B2
2022B2
2021B3
2019B1
2018B2
2017B1
2016B3

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

More Interpenetration of solids questions

Interpenetration of solids, 2 marks

What is a line of interpenetration?

  1. A hidden edge, drawn dashed on either solid
  2. The axis of the larger solid, where the two join
  3. The line where the surfaces of two solids meet
Show the answer

The line where the surfaces of two solids meet

Where one solid passes into another, the points common to both surfaces join up to form the line or curve of interpenetration.

Interpenetration of solids, 3 marks

Why are horizontal cutting planes used on an upright cone?

  1. They cut ellipses in plan
  2. They cut circles, easy to draw in plan
  3. They cut straight lines in plan
Show the answer

They cut circles, easy to draw in plan

A plane at right angles to the cone's axis cuts a circle. In plan it is drawn with a compass, so each crossing point is quick to find.

Interpenetration of solids, 2 marks

A cylinder meets a cone. In general, what is their interpenetration?

  1. A smooth curve
  2. Straight lines only
  3. A single point
Show the answer

A smooth curve

With a curved surface involved, the common points follow a curve. Plot enough points to join them smoothly.

Other Design & Communication Graphics (DCG) topics

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