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Curriculum › Grade 7 › Mathematics

Scale, Angles, Circles, and Volume

  • Grade 7
  • Mathematics
  • 7.G.B.4
  • Geometry
  • ★ Enrichment

Aligned to 7.G.B.4 — Common Core State Standards for Mathematics.

What this lesson teaches

Pi is the number you get when you divide any circle's circumference by its diameter, about 3.14. You can use it to find the circumference (pi times diameter) and the area (pi times radius squared). You can also use scale drawings and angle relationships to find unknown measures.

Worked examples

Example 1

Find the circumference of a circle with diameter 10. Multiply pi times the diameter: about 3.14 times 10 equals 31.4.

Example 2

Find the area of a circle with radius 5: A = πr² ≈ 3.14 × 25 = 78.5 square units.

Example 3

Circumference uses the radius once, area uses it twice. Doubling a circle's radius doubles the circumference but quadruples the area.

Practice questions

  1. Find the circumference of a circle with diameter 4 (use 3.14).
  2. Where does pi come from?
  3. Find the area of a circle with radius 3 (use 3.14).

Watch the lesson

Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.

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En español

Escala, Ángulos, Círculos y Volumen

Pi es el número que obtienes al dividir la circunferencia de cualquier círculo entre su diámetro, aproximadamente 3.14. Puedes usarlo para encontrar la circunferencia (pi por el diámetro) y el área (pi por el radio al cuadrado). También puedes usar dibujos a escala y relaciones entre ángulos para encontrar medidas desconocidas.

Ejemplo 1: Encuentra la circunferencia de un círculo con diámetro 10. Multiplica pi por el diámetro: aproximadamente 3.14 por 10 es igual a 31.4.

Ejemplo 2: Halla el área de un círculo de radio 5: A = πr² ≈ 3.14 × 25 = 78.5 unidades cuadradas.

Ejemplo 3: La circunferencia usa el radio una vez, el área lo usa dos. Duplicar el radio duplica la circunferencia pero cuadruplica el área.

More Geometry lessons

Scale Drawings7.G.A.1Building Triangles from Given Conditions7.G.A.2Cross Sections of Solids7.G.A.3Angle Relationships & Equations7.G.B.5Area, Volume & Surface Area7.G.B.6

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