Circumference: Application and Problem Solving Answer Key

Worksheet 3 of 5 in the Grade 7 circles series. Find the distance around a circle with $C = \pi d$ or $C = 2\pi r$, then apply it to wheels, tracks, and fences. Next: Area.

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Lesson Notes

The circumference is the perimeter of a circle: the distance you would travel walking once around its edge. Because $C \div d$ is always $\pi$, you can find the circumference of any circle from its diameter or radius.

$C = \pi d$$C = 2\pi r$(the same formula, since $d = 2r$)

Choosing the formula

Given the diameter? Use $C = \pi d$. Multiply once.
Given the radius? Use $C = 2\pi r$. Double the radius first, then multiply by $\pi$.
Given the circumference and asked for $d$ or $r$? Work backward: $d = C \div \pi$, then $r = d \div 2$ if needed.

Worked example 1: forward

Radius $= 6$ cm. Find $C$.

$C = 2\pi r = 2 \times 3.14 \times 6 = 37.68$ cm

Worked example 2: backward

$C = 50.24$ in. Find $r$.

$d = C \div \pi = 50.24 \div 3.14 = 16$ in, so $r = 16 \div 2 = 8$ in

Real-world clues

One rotation of a wheel moves it forward exactly one circumference. Distance $= C \times$ number of rotations.
Fence, border, trim, ribbon around a round object means circumference. Multiply by a price per unit to get cost.
Half a circle (semicircle) has a curved edge of $C \div 2$. Its full perimeter also includes the straight diameter.

Units matter. Circumference is a length, so the answer keeps the same unit as the radius or diameter (cm, in, m). Never square the unit here; that only happens for area.

25 problems. Show your work in the space under each problem, then put a box around your answer. On screen, the eye at the right of each problem shows or hides the worked solution.