Geometry Basics

Circle Area and Circumference

Compute A = πr² and C = 2πr for r = 5, giving A = 25π and C = 10π (π symbolic).

circle-area-circumference For a circle with radius r: - Area A = πr² (square units). - Circumference C = 2πr (distance around). - Leave π symbolic — do not approximate.

Example

Use radius formulas while keeping pi symbolic.

highlighted = computed this step

Step 1 — Radius

Set up the given values.

r=5r= 5
Start with radius r = 5.r = 5A = 25piC = 10piThe radius runs from the center to the circle.

Step 2 — Square the radius

Square the radius: 5^2 = 25.

52=255^{2} = \hl{25}
Square the radius: 5 x 5 = 25.r = 55525A = 25piC = 10pir squared gives the coefficient 25 before pi.

Step 3 — Area formula

Keep pi symbolic: A = 25pi.

A=25πA= \hlmath{25\pi}
Area uses the filled circle: A = 25pi.r = 55525A = 25piC = 10piArea is the filled inside of the circle.

Step 4 — Circumference formula

Use C = 2pi r: 2 x 5 = 10, so C = 10pi.

C=2π×5=10πC= 2 \pi \times 5 = \hlmath{10\pi}
Circumference uses the boundary: C = 10pi.r = 5diameter factor: 2 x 5 = 10A = 25piC = 10piCircumference is the length around the outside boundary.

Step 5 — Result

Read the final result.

A=25πC=10πA= 25\pi \quad C= 10\pi
Exact results: A = 25pi and C = 10pi.r = 5diameter factor: 2 x 5 = 105525A = 25piC = 10piKeep pi symbolic in the exact answer.