Area of Circles Practice Worksheet

Practice finding circle area using radius, diameter, and answers in terms of \(\pi\).

Try each problem on your own first. Then click Show solution to check the formula, substitution, and final answer.

Formula Reminder

The area of a circle is:

\[ A=\pi r^2 \]

where \(r\) is the radius of the circle.

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Level 1: Radius Given

Problem 1

Find the area of a circle with radius \(4\). Leave your answer in terms of \(\pi\).

\[ r=4 \]
Show solution

Use the area formula.

\[ A=\pi r^2 \] \[ A=\pi(4)^2 \] \[ A=16\pi \]

The area is \(16\pi\) square units.

Problem 2

Find the area of a circle with radius \(7\). Leave your answer in terms of \(\pi\).

\[ r=7 \]
Show solution
\[ A=\pi(7)^2 \] \[ A=49\pi \]

The area is \(49\pi\) square units.

Problem 3

Find the area of a circle with radius \(10\). Leave your answer in terms of \(\pi\).

\[ r=10 \]
Show solution
\[ A=\pi(10)^2 \] \[ A=100\pi \]

The area is \(100\pi\) square units.

Level 2: Diameter Given

Problem 4

Find the area of a circle with diameter \(12\). Leave your answer in terms of \(\pi\).

\[ d=12 \]
Show solution

The radius is half the diameter.

\[ r=\frac{12}{2}=6 \] \[ A=\pi(6)^2 \] \[ A=36\pi \]

The area is \(36\pi\) square units.

Problem 5

Find the area of a circle with diameter \(18\). Leave your answer in terms of \(\pi\).

\[ d=18 \]
Show solution
\[ r=\frac{18}{2}=9 \] \[ A=\pi(9)^2 \] \[ A=81\pi \]

The area is \(81\pi\) square units.

Problem 6

Find the area of a circle with diameter \(30\). Leave your answer in terms of \(\pi\).

\[ d=30 \]
Show solution
\[ r=\frac{30}{2}=15 \] \[ A=\pi(15)^2 \] \[ A=225\pi \]

The area is \(225\pi\) square units.

Level 3: Decimal Approximations

Problem 7

Find the area of a circle with radius \(5\). Use \(3.14\) for \(\pi\).

\[ r=5,\quad \pi\approx3.14 \]
Show solution
\[ A=\pi r^2 \] \[ A\approx3.14(5)^2 \] \[ A\approx3.14(25) \] \[ A\approx78.5 \]

The area is approximately \(78.5\) square units.

Problem 8

Find the area of a circle with diameter \(14\). Use \(3.14\) for \(\pi\).

\[ d=14,\quad \pi\approx3.14 \]
Show solution

First find the radius.

\[ r=\frac{14}{2}=7 \] \[ A\approx3.14(7)^2 \] \[ A\approx3.14(49) \] \[ A\approx153.86 \]

The area is approximately \(153.86\) square units.

Need more help with area of circles?

Area of circles becomes much easier when students remember that the radius is half the diameter and that area uses \(r^2\), not just \(r\). For a full explanation, visit my Area of Circles guide.

Related Geometry Resources

Area of Circles Explained

Review radius, diameter, pi, and circle area formulas.

Pythagorean Theorem

Practice another important geometry formula involving right triangles.

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