Primary 6 Area and circumference of circles
Circumference measures the distance around a whole circle. Area measures the space inside it. For part of a circle, check every edge before finding the perimeter.
Parts of a circle
Look at one part at a time. The diameter is twice the radius: d = 2r.
Try together
A circle has a diameter of 18 cm. What is its radius?
Reveal the answer
18 ÷ 2 = 9 cm.
Finding circumference and area
Use the diameter for the circumference formula, or twice the radius. Use the radius for the area formula. Follow the value of π given in the question.
Find the circumference
A circle has radius 7 cm. Find its circumference. Take π = 227.
- Find the diameter: d = 2 × 7 = 14 cm.
- Choose the formula: C = π × d.
- Calculate: C = 227 × 14 = 44 cm.
Answer: 44 cm
Find the area
The same circle has radius 7 cm. Find its area. Take π = 227.
- Choose the formula: A = π × r × r.
- Substitute: A = 227 × 7 × 7.
- Calculate: A = 154 cm².
Answer: 154 cm²
Try together
A circle has diameter 14 cm. Find its circumference and area. Take π = 227.
Reveal the answers
r = 7 cm; circumference = 44 cm; area = 154 cm².
Area and perimeter of a semicircle
A semicircle is half a circle. Its area is half the whole-circle area. Its perimeter includes the half-circle arc and the straight diameter.
Find the area
A semicircle has diameter 14 cm. Find its area. Take π = 227.
- Find the radius: r = 14 ÷ 2 = 7 cm.
- Choose the formula: A = 12 × π × r × r.
- Calculate: A = 12 × 227 × 7 × 7 = 77 cm².
Answer: 77 cm²
Find the perimeter
The same semicircle has diameter 14 cm. Find its perimeter. Take π = 227.
- Find the arc: half the circumference is 12 × 227 × 14 = 22 cm.
- Find the straight edge: the diameter is 14 cm.
- Add the edges: P = 22 + 14 = 36 cm.
Answer: 36 cm
Area and perimeter of a quarter circle
A quarter circle is one fourth of a circle. Its area is one fourth of the whole-circle area. Its perimeter includes the quarter-circle arc and two straight radii.
Find the area
A quarter circle has radius 7 cm. Find its area. Take π = 227.
- Choose the formula: A = 14 × π × r × r.
- Substitute: A = 14 × 227 × 7 × 7.
- Calculate: A = 38 12 cm².
Answer: 38 12 cm²
Find the perimeter
The same quarter circle has radius 7 cm. Find its perimeter. Take π = 227.
- Find the diameter: d = 2 × 7 = 14 cm.
- Find the arc: one fourth of the circumference is 14 × 227 × 14 = 11 cm.
- Find the straight edges: 7 + 7 = 14 cm.
- Add the edges: P = 11 + 14 = 25 cm.
Answer: 25 cm
Try together
A quarter circle has radius 14 cm. Find its perimeter. Take π = 227.
Reveal the answer
Arc = 14 × 227 × 28 = 22 cm. Two radii = 28 cm. Perimeter = 50 cm.