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. Work each one on the canvas under it (pen, eraser and clear are in the canvas toolbar; drag the handle below the canvas for more room). Enter your answer in the box (the keypad under it has fractions, exponents, square roots, pi, the degree sign and the symbols < > ≤ ≥ ≠). When a Unit row is shown, tap the unit for your answer. Then press Check. The eye at the right of the row shows or hides the worked solution.