Area of a Circle
Objective
Calculate the area of a circle
Calculate the radius from the
area
D+ Topic
Terms and Conditions
To the best of the producer's knowledge, the academic content of this presentation is accurate but errors and omissions may be present and Brain-Cells: E.Resources
Ltd cannot be held responsible for these or any lack of success experienced by individuals or groups or other parties using this material. The presentation is intended
as support material for GCSE maths and is not a comprehensive pedagogy of all the maths topics designated by the curriculum. The copyright proprietor has licensed
this presentation as an educational resource and prohibits copying or reproduction in part or whole or the publication of the material on the Internet or other media
without the written permission of Brain-Cells: E.Resouces Ltd.
© Brain-Cells: E.Resources Ltd. All Rights Reserved www.brain-cells.co.uk
What name is given to a
straight line passing
through the centre of a
circle as shown?
A. Metre
D. Circumference
C. Diameter
E. Radius
© Brain-Cells: E.Resources Ltd. All Rights Reserved www.brain-cells.co.uk
What name is given to a
straight line going from
the centre to the edge
as shown?
A. Median
D. Ellipse
C. Sector
E. Radius
© Brain-Cells: E.Resources Ltd. All Rights Reserved www.brain-cells.co.uk
∏
A special number called pi is
used when we calculate the area
of a circle. We use a Greek
letter to represent this
The
number. To 2 decimal places,
Greek
what is the value of ∏?
letter pi
A. 31.4
D. 7.38
C. 0.341
E. 3.14
© Brain-Cells: E.Resources Ltd. All Rights Reserved www.brain-cells.co.uk
Which of these
formulae would we use
to calculate the area
of a circle?
A. Area = ∏r2
D. Area = ∏d2
C. Area = 2∏r2
E. Area = 3.14∏r2
© Brain-Cells: E.Resources Ltd. All Rights Reserved www.brain-cells.co.uk
How to calculate the area of a circle
The next two slides show examples of
how the area of a circle can be
calculated…
© Brain-Cells: E.Resources Ltd. All Rights Reserved www.brain-cells.co.uk
Calculate
the area of
this circle
Always
write down
the formula
Radius = 7.6cm
A = ∏r2
Use the
given value
for r and
3.14 for ∏
A = 3.14 x 7.62
Don’t forget
to write in
the units and
accuracy
A = 3.14 x 57.76
Workout
A = 181.37 cm2 (to 2 d.p.)
© Brain-Cells: E.Resources Ltd. All Rights Reserved www.brain-cells.co.uk
Diameter = 22 cm
Calculate
the area of
this circle
Radius is
22 ÷ 2 = 11 cm
A = ∏r2
If you are
given the
diameter,
divide it by 2
to get the
radius
A = 3.14 x 112
Don’t forget
to write in
the units and
accuracy
A = 3.14 x 121
Workout
A = 379.94 cm2 (to 2 d.p.)
© Brain-Cells: E.Resources Ltd. All Rights Reserved www.brain-cells.co.uk
The next slide shows the radius of
four circles and diameter of four
circles.
Using the approximation of 3.14
for ∏, calculate the area of the
circles giving your answer to 2 d.p.
© Brain-Cells: E.Resources Ltd. All Rights Reserved www.brain-cells.co.uk
Calculate to 2 d.p. the areas of these circles
1. Radius = 10 cm
2. Radius = 15 cm
3. Radius = 13.5 cm
4. Radius = 8.75 cm
5. Diameter = 24 cm
6. Diameter = 21 cm
Diameter = 22 cm
Calculate
the area of
this circle
Radius is
22 ÷ 2 = 11 cm
A = ∏r2
If you are
given the
diameter,
divide it by 2
to get the
radius
A = 3.14 x 112
Don’t forget
to write in
the units and
accuracy
A = 3.14 x 121
Workout
A = 379.94 cm2 (to 2 d.p.)
© Brain-Cells: E.Resources Ltd. All Rights Reserved www.brain-cells.co.uk
7. Diameter = 3.8 cm
8. Diameter = 2.5 cm
© Brain-Cells: E.Resources Ltd. All Rights Reserved www.brain-cells.co.uk
Calculate to 2 d.p. the areas of these circles
1. Radius = 10 cm  Area = 314.00 cm2 (to 2 d.p.)
2. Radius = 15 cm  Area = 706.50 cm2 (to 2 d.p.)
3. Radius = 13.5 cm  Area = 572.27 cm2 (to 2 d.p.)
4. Radius = 8.75 cm  Area = 240.41 cm2 (to 2 d.p.)
5. Diameter = 24 cm  Area = 452.16 cm2 (to 2 d.p.)
6. Diameter = 21 cm  Area = 346.19 cm2 (to 2 d.p.)
7. Diameter = 3.8 cm  Area = 11.34 cm2 (to 2 d.p.)
8. Diameter = 2.5 cm  Area = 4.91 cm2 (to 2 d.p.)
© Brain-Cells: E.Resources Ltd. All Rights Reserved www.brain-cells.co.uk
Calculating the Radius from the Area
Sometimes, we know the area and
need to calculate the radius.
We can do this using the formula:
r = √(A ÷ π)
© Brain-Cells: E.Resources Ltd. All Rights Reserved www.brain-cells.co.uk
For example, what is
the radius of a circle
with an area of 120
cm2?
Write down
the formula
Put in the
numbers
Area is
120 cm2
r = √(A ÷ π)
r = √( 120 ÷ 3.14)
r = √38.217
Workout
r = 6.18 cm to 2 d.p.
© Brain-Cells: E.Resources Ltd. All Rights Reserved www.brain-cells.co.uk
Calculate to 2 d.p. the radii of these circles
1. Area = 40 cm2
2. Area = 46.6 cm2
3. Area = 53.5 cm2
4. Area = 475 cm2
5. Area = 34.7
cm2
6. Area = 215 cm2
7. Area = 686
cm2
For example, what is
the radius of a circle
with an area of 120
cm2?
Write down
the formula
Put in the
numbers
Area is
120 cm2
r = √(A ÷ π)
r = √( 120 ÷ 3.14)
r = √38.217
Workout
r = 6.18 cm to 2 d.p.
© Brain-Cells: E.Resources Ltd. All Rights Reserved www.brain-cells.co.uk
8. Area = 75.5 cm2
© Brain-Cells: E.Resources Ltd. All Rights Reserved www.brain-cells.co.uk
Calculate to 2 d.p. the radii of these circles
1. Area = 40 cm2  Radius = 3.57 cm (to 2 d.p.)
2. Area = 46.6 cm2  Radius = 3.85 cm (to 2 d.p.)
3. Area = 53.5 cm2  Radius = 4.13 cm (to 2 d.p.)
4. Area = 475 cm2  Radius = 12.30 cm (to 2 d.p.)
5. Area = 34.7 cm2  Radius = 3.32 cm (to 2 d.p.)
6. Area = 215 cm2  Radius = 8.27 cm (to 2 d.p.)
7. Area = 686 cm2  Radius = 14.78 cm (to 2 d.p.)
8. Area = 75.5 cm2  Radius = 4.90 cm (to 2 d.p.)
© Brain-Cells: E.Resources Ltd. All Rights Reserved www.brain-cells.co.uk