Unroll the rim, crack the case — where π leaves its fingerprints on everything round.
REMEMBER: The diameter is two radii. Circumference
C = πd measures around; area A = πr² fills inside
(square the radius — never double it). Angles on a straight line total
180°, around a point 360°, and vertical angles
are twins.
Part 1 · The Circle Unroller
Where do the circle formulas come from? Unroll and see! Set the radius, then
switch views: unroll the rim to discover how many diameters
fit around the edge, or slice the inside into wedges and lay
them flat to see where πr² is hiding.
Radius:4
Part 2 · The Angle Detective
One angle is known. One is a mystery. Study the diagram, deduce the relationship
— straight line? right angle? vertical twins? — and type your answer.
Lock It In before the reveal!
Cases solved: 0
Part 3 · The Detective's Toolkit
Three tools for three kinds of case. Each one prints every step, the
why, and the right units.
Tell the machine what you know — it sorts out radius vs. diameter FIRST, then computes both C and A (using π ≈ 3.14).
Pick the relationship, enter the known angle, and the solver writes the equation and finds x.
A rectangular prism (a box). The machine finds the volume (what FILLS it) and the surface area (what WRAPS it) — and never mixes up the units.
Part 4 · Chief Detective Quiz
Question 1 of 10Score: 0
📗 Word Box
Radius (r)
The distance from the center of a circle to its edge. The circle's most important measurement.
Diameter (d)
The distance all the way across, through the center. Always exactly two radii: d = 2r.
Circumference (C)
The distance around the rim of a circle — its perimeter. Unrolled, it's a bit more than 3 diameters long.
Pi (π)
The number of diameters that wrap around any circle: about 3.14. Every circle in the universe uses the same π.
Supplementary angles
Two angles that add to 180° — together they fill a straight line.
Complementary angles
Two angles that add to 90° — together they fill a right angle's corner.
Vertical angles
The opposite angles formed when two lines cross. They are always equal — perfect twins.
Volume & surface area
Volume is the space INSIDE a solid (cubic units, like cm³). Surface area is the total area of all its faces — the wrapping (square units, like cm²).