Circle Circumference and Area

What you’ll learn

Use radius and diameter correctly in circle formulas.

ប្រើកាំ និងអង្កត់ផ្ចិតត្រឹមត្រូវក្នុងរូបមន្តរង្វង់។

Meaning and use

The radius joins the centre to the circle; the diameter passes through the centre and is twice the radius. Circumference is boundary length, while area is the enclosed surface. Keep pi symbolic for an exact result, or state the approximation used.

កាំពីផ្ចិតទៅរង្វង់ ហើយអង្កត់ផ្ចិតស្មើពីរដងកាំ។ បរិមាត្រជាប្រវែងជុំវិញ និងផ្ទៃក្រឡាជាផ្ទៃខាងក្នុង។ អាចទុក π សម្រាប់ចម្លើយពិតប្រាកដ។

Formulas

Diameter and circumference

\[d=2r,\qquad C=2\pi r=\pi d\]

Circle area

\[A=\pi r^2\]

Symbols and units

Symbol	Meaning	Unit or restriction
r	Radius	Length unit
d	Diameter	Same length unit as r
C	Circumference	Length unit
A	Circle area	Square length unit
π	Circle constant, approximately 3.14159	Dimensionless

Conditions and limits

• These formulas apply to a full circle.
• If a diameter is given, halve it before using the radius-based area formula.
• កុំបង្គត់ π មុនពេលដែលចាំបាច់។

Worked examples

Circumference from radius

A circle has radius 7 cm.

1. Use \(C=2\pi r\).
2. Substitute \(C=2\pi\times7=14\pi\) cm.
3. Using \(\pi\approx3.14\), get \(C\approx43.96\) cm.

\(14\pi\,\mathrm{cm}\) (about 43.96 cm)

បរិមាត្រជាឯកតាប្រវែង មិនមែនការ៉េ។

Area from diameter

A circle has diameter 10 m.

1. Radius \(r=10/2=5\) m.
2. Area \(A=\pi\times5^2=25\pi\) m².
3. With \(\pi\approx3.14\), \(A\approx78.5\) m².

\(25\pi\,\mathrm{m^2}\) (about 78.5 m²)

ត្រូវបម្លែងអង្កត់ផ្ចិតទៅកាំមុនគុណការ៉េ។

Common mistakes

Instead of	Use	Why
For diameter 10, area = π × 10².	For diameter 10, area = π × 5².	The area formula uses radius.
Circumference is measured in cm².	Circumference is measured in cm.	Circumference is a length.

Practice

Solve these before revealing the worked solutions. Include units where relevant.

សាកល្បងដោះស្រាយមុនបើកមើលចម្លើយ។ សូមបង្ហាញជំហាន និងឯកតាដែលពាក់ព័ន្ធ។

1. Find the diameter when r = 4 cm.
2. Find the circumference when d = 6 m. Leave pi exact.
3. Find the area when r = 3 cm. Leave pi exact.

Answers and steps

Show solutions / បង្ហាញដំណោះស្រាយ

1. 8 cm

   d = 2r = 2 × 4.

2. 6π m

   C = πd.

3. 9π cm²

   A = πr² = π × 9.

Quick recap

• Diameter is twice radius.
• Circumference uses linear units and area uses square units.
• State whether pi is exact or approximated.