11-14-2025, 10:29 PM
[border]TIER 8 — Advanced Modelling[/border]
Tier 8 — Challenge 001 — The Thermal Plateau Problem
A metal plate is heated at the centre and cools toward the edges.
The temperature at a distance r from the centre is modelled by:
T® = 180 − 25 ln(1 + r)
Where:
• T® is temperature in °C
• r is distance in centimetres (0 ≤ r ≤ 10)
Questions:
1. What is the temperature at r = 6 cm?
2. At what distance r does the plate reach **120°C**?
(Solve exactly or with a calculated approximation.)
3. The safe operating region requires temperatures under 110°C.
For what range of r is the plate unsafe?
Explain your reasoning clearly.
? Submit Your Attempt
Thread title:
Tier 8 Attempt — YourUsername — Challenge 001
Tier 8 — Challenge 001 — The Thermal Plateau Problem
A metal plate is heated at the centre and cools toward the edges.
The temperature at a distance r from the centre is modelled by:
T® = 180 − 25 ln(1 + r)
Where:
• T® is temperature in °C
• r is distance in centimetres (0 ≤ r ≤ 10)
Questions:
1. What is the temperature at r = 6 cm?
2. At what distance r does the plate reach **120°C**?
(Solve exactly or with a calculated approximation.)
3. The safe operating region requires temperatures under 110°C.
For what range of r is the plate unsafe?
Explain your reasoning clearly.
? Submit Your Attempt
Thread title:
Tier 8 Attempt — YourUsername — Challenge 001