L5 · Circumference and Composite Perimeters

Learning goal

“I can find the circumference of a circle from its diameter or radius and work backwards from a circumference; find the perimeter of semicircles and composite shapes that mix straight edges with circular arcs; and describe a measuring strategy for the perimeter of an irregular object.”

Circumference — the perimeter of a circle: C = pi x d = 2 x pi x r, with pi about 3.14 here.

Semicircle — exactly half a circle; its perimeter is half the circumference PLUS the straight diameter edge.

Composite shape — a shape built from two or more simpler shapes; its perimeter counts only the outside boundary - internal shared edges are never counted.

Worked example

A circle has diameter 14 cm. C = pi x d = 3.14 x 14 = 43.96 cm. Given radius instead: r = 6 m -> C = 2 x pi x r = 2 x 3.14 x 6 = 37.68 m. Backwards: C = 62.8 m -> d = C / pi = 62.8 / 3.14 = 20 m. Say it plainly (from Grade 7, still true): pi multiplies the DIAMETER; choose the formula by what you are given, and undo with division.

Check yourself — explain it

A student answers Q1-type problems correctly but always doubles the radius first, even when given the diameter. Why is that risky?

Paired problem — example still visible

r = 10 cm -> C -> 62.8 cm

Faded completion — last step is yours

"C = 31.4 cm, so d = 31.4 / 3.14 = ___ cm" -> 10 cm

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

Start practice →Take the unit quiz

Grade 10 — Mathematics 10C › C10U01 Measurement Systems & Conversions

L5 · Circumference and Composite Perimeters