Topics › KS3 › Geometry & measures

Circumference

1. cfr-01 Present from here

   A circle has diameter $10\text{ cm}$. What is its circumference, in terms of $\pi$?

   A Option A: $10\pi\text{ cm}$

   B Option B: $20\pi\text{ cm}$

   C Option C: $5\pi\text{ cm}$

   D Option D: $25\pi\text{ cm}$
   Answer and misconceptions

   A Option A: $10\pi\text{ cm}$ ✓ Correct

   B Option B: $20\pi\text{ cm}$ ✗

   Uses the diameter as the radius in $2\pi r$Works out $2 \times \pi \times 10$; the radius is $5$, so $2\pi r = \pi d = 10\pi$.

   C Option C: $5\pi\text{ cm}$ ✗

   Multiplies $\pi$ by the radiusWorks out $\pi \times 5$; circumference is $\pi \times$ diameter, or $2 \times \pi \times$ radius.

   D Option D: $25\pi\text{ cm}$ ✗

   Uses the area formulaWorks out $\pi r^2 = \pi \times 5^2$, which is the area, not the distance round the edge.
2. cfr-02 Present from here

   A circle has radius $4\text{ cm}$. Using $\pi = 3.14$, what is its circumference?

   A Option A: $12.56\text{ cm}$

   B Option B: $50.24\text{ cm}$

   C Option C: $25.12\text{ cm}$

   D Option D: $8\text{ cm}$
   Answer and misconceptions

   A Option A: $12.56\text{ cm}$ ✗

   Multiplies $\pi$ by the radius instead of the diameterWorks out $3.14 \times 4$; the diameter is $8$, so $3.14 \times 8 = 25.12$.

   B Option B: $50.24\text{ cm}$ ✗

   Uses the area formulaWorks out $3.14 \times 4^2$, which is the area.

   C Option C: $25.12\text{ cm}$ ✓ Correct

   D Option D: $8\text{ cm}$ ✗

   Gives the diameter instead of the circumferenceDoubles the radius to get the diameter, $8\text{ cm}$, but does not multiply by $\pi$.
3. cfr-03 Present from here

   A circle has circumference $18\pi\text{ cm}$. What is its radius?

   A Option A: $18\text{ cm}$

   B Option B: $9\text{ cm}$

   C Option C: $36\text{ cm}$

   D Option D: $\sqrt{18}\text{ cm}$
   Answer and misconceptions

   A Option A: $18\text{ cm}$ ✗

   Gives the diameter instead of the radius$\pi d = 18\pi$ gives $d = 18$; the radius is half of that.

   B Option B: $9\text{ cm}$ ✓ Correct

   C Option C: $36\text{ cm}$ ✗

   Doubles instead of halvingThinks the radius is twice the diameter; the radius is half the diameter.

   D Option D: $\sqrt{18}\text{ cm}$ ✗

   Treats the circumference as an area and square rootsUses $\pi r^2 = 18\pi$; that formula is for area, not circumference.
4. cfr-04 Present from here

   A semicircle has diameter $12\text{ cm}$. What is its perimeter, in terms of $\pi$?

   A Option A: $6\pi\text{ cm}$

   B Option B: $(6\pi + 6)\text{ cm}$

   C Option C: $(12\pi + 12)\text{ cm}$

   D Option D: $(6\pi + 12)\text{ cm}$
   Answer and misconceptions

   A Option A: $6\pi\text{ cm}$ ✗

   Forgets the straight edgeFinds the curved part, $6\pi$, but the perimeter also includes the diameter, $12\text{ cm}$.

   B Option B: $(6\pi + 6)\text{ cm}$ ✗

   Uses the radius for the straight edgeThe straight edge of a semicircle is the whole diameter, $12\text{ cm}$, not the radius.

   C Option C: $(12\pi + 12)\text{ cm}$ ✗

   Uses the circumference of the whole circleUses $12\pi$ for the curved part; a semicircle has half of it, $6\pi$.

   D Option D: $(6\pi + 12)\text{ cm}$ ✓ Correct
5. cfr-05 Present from here

   A bicycle wheel has diameter $70\text{ cm}$. How far does the bicycle travel when the wheel turns once? Use $\pi = \frac{22}{7}$.

   A Option A: $110\text{ cm}$

   B Option B: $440\text{ cm}$

   C Option C: $220\text{ cm}$

   D Option D: $3850\text{ cm}$
   Answer and misconceptions

   A Option A: $110\text{ cm}$ ✗

   Multiplies $\pi$ by the radiusWorks out $\frac{22}{7} \times 35$; one turn is the circumference, $\pi \times 70$.

   B Option B: $440\text{ cm}$ ✗

   Uses $2\pi$ with the diameterWorks out $2 \times \frac{22}{7} \times 70$; the formula $2\pi r$ uses the radius, not the diameter.

   C Option C: $220\text{ cm}$ ✓ Correct

   D Option D: $3850\text{ cm}$ ✗

   Finds the area instead of the distance round the edgeWorks out $\frac{22}{7} \times 35^2$, which is the area of the wheel.