

Area of a Circle and its formulaPractice Problems & examplesFormula for Area of circle:The formula to find a circle's area$$ \pi \cdot$$(radius)^{2} usually expressed as $$ \pi \cdot r^2 $$ where r is the radius of a circle. The area of a circle is all the space inside a circle's circumference.
Practice Problems
Explore and discover the relationship bet wen the area formula , the radius of a circle and its graph with with our interactive applet Problem 1) What is the area of the circle on the left? Round your answer to the nearest tenth.
Remember the Formula: $$ Area = \pi \cdot r^2 \\ A = \pi \cdot ( 22')^2 \\ A = \pi \cdot 1,520 \text{ square feet} \\ A = 4775.220833456486\text{ square feet} \\ Area = \boxed{ 4775.2 } $$ Problem 2
What is this circle's area? Round your answer to the nearest tenth.
$$
Area = \pi \cdot r^2
\\
A = \pi \cdot ( 5")^2
\\
A = \pi \cdot 25 \text{ square inches}
\\
A = 78.53981633974483 \text{square inches}
\\
A = 78.5 \text{ square inches, rounded to nearest tenth}
$$
Problem 3
What is the area of a circle with a radius of 7 centimeters? Round your answer to the nearest hundredth
$$
Area = \pi \cdot r^2
\\
A = \pi \cdot (7 \text{ centimeters} )^2
\\
A = 153.93804002589985 \text{ square centimeters}
\\
\boxed { A = 153.94 \text{ square centimeters, rounded to nearest hundredth}}
\\
$$
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.$$ A = \pi r^2 \\ 120 = \pi r^2 \\ \frac{120}{\pi} = r^2 \\ 38.197 = r^2 \\ \sqrt{38.197} = r \\ \boxed {r=6.18 \text{ inches }} $$ Problem 5 What is the diameter of a circle if its area is 360 in^{2}? (Round your answer to the nearest hundredth of an inch)
Like the last problem, we are given area and need to solve for radius ; However, this time, we need to then do one more step  find the diameter$$ A = \pi r^2 \\ 360 in^2= \pi r^2 \\ \frac{360}{\pi} = r^2 \\ 114.59155902616465= r^2 \\ \sqrt{114.59155902616465} = r \\ r=10.704744696916627 \text{ inches } \\ $$ Now, that'we found the radius, how do we find the diameter?
$$
diameter = 2 \cdot radius
\\
= 2 \cdot 10.704744696916627
\\
=21.409489393833255
\\
\boxed{diameter =21.41 \text{ inches, rounded to nearest hundredth}}
$$
Challenge Problems
Problem 6
A circle has a diameter of 12 inches. What is its area in terms of $$\pi$$ . (Need a hint) Remember: the formula for the area of a circle is based on the circle's radius not its diameter.
Problem 7 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 doubling 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
Back to
Circles 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 interactive applet 