Lesson · Grade 7 · Mathematics
Why the Area of a Circle Is π × r × r
- Grade 7
- Mathematics
- 1 min 21 s
- British Columbia
- BC7-MA-50
A circle is cut into equal wedges that are laid in a row, tips up and down, and with thinner wedges the row becomes almost a rectangle as tall as the radius and as long as half the circumference, so its area, and the circle's, is π × r × r. A worked example with a 5 cm radius gives π × 5 × 5 ≈ 3.14 × 25 = 78.5 cm², and the video ends on the recap Area = π × r × r.
Concept: Why the area of a circle is pi x r x r
Anyone can watch two lessons on the website without an account. Signing in is free, no payment and no card, and opens three a day; Plus has no limit.
Loading
In one sentence
The question this lesson answers
Why is the area of a circle pi times r times r?
The radius, r, goes from the centre of the circle to its edge.
Transcript
What the lesson says
Why is the area of a circle pi times r times r?
The radius, r, goes from the centre of the circle to its edge.
The distance around the circle is 2 times pi times r.
Cut the circle into 16 equal wedges.
Lay the wedges in a row, with the tips pointing up and down.
With thinner wedges, the shape is almost a rectangle.
Its height is the radius, r.
Its length is half the distance around the circle.
Half of 2 times pi times r is pi times r.
Its area is length times height, which is pi times r times r.
The circle is made of the same wedges, so it has the same area.
Now try a circle with a radius of 5 centimetres.
Its area is pi times 5 times 5.
Pi is about 3.14, and 5 times 5 is 25.
So the area is about 78.5 square centimetres.
Remember, the area of a circle is pi times r times r.
Curriculum
Where this fits
- British Columbia, Grade 7
Mathematics, Geometry and measurement: circumference and area of circlesBC7-MA-50
Previous: Diameter from circumferenceNext: Area of a Circle from the Radius or the Diameter
The outcomes and strands follow the British Columbia curriculum.
Keep going
1 min 12 s3:15 p.m. or 15:15? Morning, afternoon and the 24-hour clock
Grade 4 · 1 min 12 s
1 min 26 s3D Objects: Faces, Edges and Vertices
Grade 3 · 1 min 26 s
1 min 21 sArea and Perimeter: What Is the Difference?
Grade 5 · 1 min 21 s
1 min 5 sArea of a Circle from the Radius or the Diameter
Grade 7 · 1 min 5 s
1 min 14 sArea of a Parallelogram: Cut and Slide into a Rectangle
Grade 6 · 1 min 14 s
1 min 18 sArea of a Rectangle: Count the Squares, Then Multiply
Grade 5 · 1 min 18 s
1 min 16 sArea of a Trapezoid: Two Copies Make a Parallelogram
Grade 6 · 1 min 16 s
1 min 19 sArea of a Triangle: Half of a Parallelogram
Grade 6 · 1 min 19 s
- All Grade 7 Mathematics lessons
- Teachers: the maths worksheets for Grade 7 are in the dashboard, each with a worked example and a proven answer key.
- Try the graph paper, free for everyone, no account needed.
- Create a free account to watch three lessons a day, no payment and no card.