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Area of a Circle and its formula
Practice Problems & examples
Formula for Area of circle:
The formula to find a circle's area : π×(radius)2 usually expressed as Πr2 where r is the radius of a circle.
The area of a circle is all the space inside a
circle's circumference.
Practice Problems
 
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In the picture on the left, the area of the circle is the part of the circle that is changing color. |
Interactive Area of a Circle
(View applet on its own page)
Explore and discover the relationship between area,
radius and graph of a circle. .
Just click and drag the points.
Radical Form?
$$ Area = \pi \cdot radius^2 $$
$$ $$
$$ $$
Problem 1)
What is the area of the circle on the left?
| Answer |
Remember the Formula:
A= Π×radius2
A = (22')2 ×Π = 484Π square feet ≈ 1,520 square feet
Problem 2
What is this circle's area?
Remember the
Formula:
A= Π×radius2
A = (5")2 • Π = 25Π square inches ≈ 79 square inches
What is this circle's area?
| Answer |
A= Π×radius2
A = (5")2 • Π = 25Π square inches ≈ 79 square inches
Problem 3
What is the area of a circle with a radius of 7 centimeters?
A = Π(7
centimeters)2 = 49 Π centimeters squared ≈ 153 square
centimeters
Problem 4
What is the radius of a circle if its area is 120 in2? (Round your answer to the nearest hundredth of an inch)
What is the area of a circle with a radius of 7 centimeters?
| Answer |
Problem 4
What is the radius of a circle if its area is 120 in2? (Round your answer to the nearest hundredth of an inch)
| Answer |
Use the area formula ...but this time solve the radius.$$ A = \Pi r^2 \\ 120 = \Pi r^2 \\ \frac{120}{\Pi} = r^2 \\ 38.197 = r^2 \\ \sqrt{38.197} = r \\ r=6.18 \text{ inches } $$
Challenge Problems
Problem 5
A circle has a diameter of 12 inches. Calculate its area. (Need a hint)
Remember: the fomula for the area of a circle is based on the circle's radius not its diameter.
Problem 6
If a circle's radius is doubled, then how much did its area increase?
Since the formula for the area of a circle squares the radius, the area of the larger circle is always 4 (or 22) times the smaller circle. Think about it: You are doubleing a number (which means ×2) and then squaring this (ie squaring 2) --which leads to a new area that is four times the smaller one.
You can see this relationship is true if you pick some actual values for the radius of a circle.
For instance, let's make the original radius = 3.
This relationship holds true no matter what radius you pick
Let's make the original radius = 5.
A circle has a diameter of 12 inches. Calculate its area. (Need a hint)
Remember: the fomula for the area of a circle is based on the circle's radius not its diameter.
| Answer |
| 1) Divide Diameter in half to calculate radius: | Radius = diameter/2 = 12/2 = 6 |
| 2) Use area formula | Area= Π ×(r)2 = Π(6)2= 36Π |
Problem 6
If a circle's radius is doubled, then how much did its area increase?
| Answer |
Since the formula for the area of a circle squares the radius, the area of the larger circle is always 4 (or 22) times the smaller circle. Think about it: You are doubleing a number (which means ×2) and then squaring this (ie squaring 2) --which leads to a new area that is four times the smaller one.
You can see this relationship is true if you pick some actual values for the radius of a circle.
For instance, let's make the original radius = 3.
| Smaller Circle | Larger Circle |
| radius =3 | radius =3*2=6 |
| A = Π(3)2 | A = Π(6)2 |
| A = 9 Π | A = 36Π |
A = 9 Π × 4 = 36 Π
This relationship holds true no matter what radius you pick
Let's make the original radius = 5.
| Smaller Circle | Larger Circle |
| radius =5 | radius =5×2= 10 |
| A = Π(5)2 | A = Π(10)2 |
| A = 25Π | A = 100Π |
A = 25Π × 4 = 100 Π
This page: Formula for area of circle
Related Pages: Mixed Practice(area, circumference) | standard form equation for a circle |arc| chord |circumference | intersection of chords within circle