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Subjects · Leaving Cert Design & Communication Graphics (DCG)

Leaving Cert Design & Communication Graphics (DCG): Solids in contact

How often Solids in contact comes up on the Design & Communication Graphics papers, every year it was asked, and questions to try.

HL Asked on 2 of the last 9 Higher Level papers, most recently in 2024.

OL Asked on 7 of the last 9 Ordinary Level papers, most recently in 2023. most years

Solids in contact, Higher Level(7 marks)

Quick ones on Solids in contact.

(a)Two spheres touch each other. Where is their point of contact?
  1. Directly above the lower centre
  2. On the line joining their centres
  3. On the HP beneath the centres
(b)A sphere touches a flat plane. Where is the point of contact?
  1. The nearest corner or edge of the flat plane
  2. Directly below the centre, whatever the plane's slope
  3. The foot of the perpendicular from the centre
(c)Spheres of radius 9 mm and 4 mm rest on the HP and touch each other. How far apart are their centres in plan?
  1. 12 mm
  2. 5 mm
  3. 13 mm
Show the answers

(a) On the line joining their centres

(b) The foot of the perpendicular from the centre

(c) 12 mm

Your turn: Higher Level questions on Solids in contact.

Higher Level

Asked on 2 of the last 9 Higher Level papers, most recently in 2024.

Every paper, year by year

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

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

Ordinary Level

Asked on 7 of the last 9 Ordinary Level papers, most recently in 2023. most years

Every paper, year by year

YearWhere it came up
2025Not asked
2024Not asked
2023A3
2022A3
2021A4
2019A1
2018A2
2017A4
2016A3

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

More Solids in contact questions

Solids in contact, 2 marks

Two spheres touch. Where is their point of contact?

  1. Directly above the smaller centre
  2. Midway between their lowest points
  3. On the line joining their centres
Show the answer

On the line joining their centres

At the contact point both radii are at 90 degrees to the shared tangent plane, so the point lies on the straight line joining the centres.

Solids in contact, 2 marks

A sphere of radius 25 mm rests on the HP. How high is its centre?

  1. 12.5 mm
  2. 25 mm
  3. 50 mm
Show the answer

25 mm

The sphere touches the HP directly below its centre, so the centre is exactly one radius above the ground.

Solids in contact, 2 marks

A sphere of radius 30 mm touches both the HP and the VP. Where is its centre?

  1. 30 mm above the HP and 30 mm in front of the VP
  2. 60 mm above the HP and 60 mm in front of the VP
  3. 15 mm above the HP and 15 mm in front of the VP
Show the answer

30 mm above the HP and 30 mm in front of the VP

Each surface a sphere touches is one radius from its centre, so the centre is 30 mm from the HP and 30 mm from the VP.

Other Design & Communication Graphics (DCG) topics

All of Leaving Cert Design & Communication Graphics (DCG)