

Area of a Circle and its formulaPractice Problems & examplesFormula for Area of circle:The formula to find a circle's area : π×(radius)^{2} usually expressed as Πr^{2} where r is the radius of a circle. The area of a circle is all the space inside a circle's circumference.
Practice Problems
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?
Remember the Formula: A= Π×radius^{2} A = (22')^{2 }×Π = 484Π square feet ≈ 1,520 square feet Problem 2
What is this circle's area?
A= Π×radius^{2} 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?
Problem 4 What is the radius of a circle if its area is 120 in^{2}? (Round your answer to the nearest hundredth of an inch)
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 2^{2}) 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.
A = 9 Π × 4 = 36 Π This relationship holds true no matter what radius you pick Let's make the original radius = 5.
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 