Topics › KS3 › Geometry & measures

Area of circles

1. circ-01 Present from here

   A circle has radius $5\text{ cm}$. What is its area, in terms of $\pi$?

   A Option A: $10\pi\text{ cm}^2$

   B Option B: $25\pi\text{ cm}^2$

   C Option C: $100\pi\text{ cm}^2$

   D Option D: $5\pi\text{ cm}^2$
   Answer and misconceptions

   A Option A: $10\pi\text{ cm}^2$ ✗

   Confuses area with circumferenceUses 2πr = 10π, the circumference formula.

   B Option B: $25\pi\text{ cm}^2$ ✓ Correct

   C Option C: $100\pi\text{ cm}^2$ ✗

   Doubles the radius before squaringUses the diameter, 10, in πr², giving π × 10².

   D Option D: $5\pi\text{ cm}^2$ ✗

   Forgets to square the radiusCalculates π × 5 instead of π × 5².
2. circ-02 Present from here

   What is the area of this circle, in terms of $\pi$?

   
   A Option A: $16\pi\text{ cm}^2$

   B Option B: $64\pi\text{ cm}^2$

   C Option C: $8\pi\text{ cm}^2$

   D Option D: $32\pi\text{ cm}^2$
   Answer and misconceptions

   A Option A: $16\pi\text{ cm}^2$ ✓ Correct

   B Option B: $64\pi\text{ cm}^2$ ✗

   Uses the diameter as the radiusCalculates π × 8²; the radius is half the diameter, 4 cm.

   C Option C: $8\pi\text{ cm}^2$ ✗

   Confuses area with circumferenceUses πd = 8π, the circumference formula.

   D Option D: $32\pi\text{ cm}^2$ ✗

   Halves after squaring the diameterCalculates π × 8² ÷ 2 instead of π × (8 ÷ 2)².
3. circ-03 Present from here

   A circle has radius $3\text{ cm}$. Use the $\pi$ button to find its area, to 1 decimal place.

   A Option A: $18.8\text{ cm}^2$

   B Option B: $113.1\text{ cm}^2$

   C Option C: $28.3\text{ cm}^2$

   D Option D: $9.4\text{ cm}^2$
   Answer and misconceptions

   A Option A: $18.8\text{ cm}^2$ ✗

   Confuses area with circumferenceCalculates 2 × π × 3 = 18.8, the circumference.

   B Option B: $113.1\text{ cm}^2$ ✗

   Doubles the radius before squaringCalculates π × 6², using the diameter in place of the radius.

   C Option C: $28.3\text{ cm}^2$ ✓ Correct

   D Option D: $9.4\text{ cm}^2$ ✗

   Forgets to square the radiusCalculates π × 3 = 9.4 instead of π × 3².
4. circ-04 Present from here

   What is the area of this semicircle, in terms of $\pi$?

   
   A Option A: $16\pi\text{ cm}^2$

   B Option B: $4\pi\text{ cm}^2$

   C Option C: $32\pi\text{ cm}^2$

   D Option D: $8\pi\text{ cm}^2$
   Answer and misconceptions

   A Option A: $16\pi\text{ cm}^2$ ✗

   Finds the area of the whole circleCalculates π × 4² but forgets to halve for a semicircle.

   B Option B: $4\pi\text{ cm}^2$ ✗

   Divides by 4 for a semicircleCalculates π × 4² ÷ 4, the area of a quarter circle.

   C Option C: $32\pi\text{ cm}^2$ ✗

   Uses the diameter as the radiusCalculates π × 8² ÷ 2, doubling the 4 cm radius first.

   D Option D: $8\pi\text{ cm}^2$ ✓ Correct
5. circ-05 Present from here

   A circle has area $49\pi\text{ cm}^2$. What is its radius?

   A Option A: $7\text{ cm}$

   B Option B: $49\text{ cm}$

   C Option C: $24.5\text{ cm}$

   D Option D: $14\text{ cm}$
   Answer and misconceptions

   A Option A: $7\text{ cm}$ ✓ Correct

   B Option B: $49\text{ cm}$ ✗

   Forgets to square rootSees πr² = 49π and gives r = 49 instead of r² = 49.

   C Option C: $24.5\text{ cm}$ ✗

   Thinks squaring means doublingHalves 49 to undo r², treating r² as 2r.

   D Option D: $14\text{ cm}$ ✗

   Gives the diameter, not the radiusFinds r = 7 correctly, then doubles it.