Circle measure modelling

Objective. Solve design and optimisation problems involving circles.

1. Learn
2. Worked example
3. Practice
4. Feedback
5. Continue

Learn: the key idea

Circle measure modelling applies arc, sector, cone and sphere formulae to real design or optimisation contexts, often requiring you to set up and solve an equation from a stated constraint. Translate the physical situation into a formula involving π, then manipulate it algebraically to find an unknown dimension. For example, if a cylindrical container must hold a fixed volume, set πr²h equal to that volume and solve for h in terms of r. Always state units clearly and check the answer makes physical sense, like a positive length.

Worked example

A cylindrical water tank must have volume 2000π cm³ and radius 10 cm. Use circle measure modelling to find the required height of the tank.

1 $Volume formula: V = πr²h$
2 $2000π = π(10²)h = 100πh$
3 $Divide both sides by 100π: h = 2000π/100π$
4 $h = 20 cm$

Answer: 20 cm

Concept mastery

Based on your past attempts at this lesson — the question types to practise again come first.

Complete a practice set to see your concept breakdown here.

Practice

Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.

Start practising

Common mistake. Students sometimes forget to check whether a found value is physically sensible, such as a negative or oversized radius for the container described, which signals an algebra or setup error that needs revisiting.

Your progress

Tick each step as you finish it. Your exact reading position is saved automatically, so Continue drops you back on the same line.

0 of 5 steps complete

Your place saves automatically as you read.

My dashboard