Area, Volume & Surface Area
Aligned to 7.G.B.6 — Common Core State Standards for Mathematics.
What this lesson teaches
The area of a circle is π × r²; the volume of a right prism is (base area) × height; surface area is the sum of the areas of every face. Choose the formula that fits the figure.
Worked examples
Example 1
A right rectangular prism is 5 cm by 3 cm by 4 cm. Volume = 5 × 3 × 4 = 60 cm³. Surface area = 2(5×3 + 5×4 + 3×4) = 2(15 + 20 + 12) = 94 cm².
Example 2
A triangular prism has a triangle base of area 6 cm² and a length of 10 cm. Volume = 6 × 10 = 60 cm³.
Example 3
Volume is measured in cubic units and surface area in square units. If your answer's unit does not match the question, the formula was wrong.
Practice questions
- Find the area of a circle with radius 7 cm. Use π ≈ 3.14.
- A triangular prism has a base area of 12 cm² and length 9 cm. Find its volume.
- Find the surface area of a cube with edge 6 cm.
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.
▶ Watch this lessonEn español
Área, Volumen y Área Superficial
El área de un círculo es π × r²; el volumen de un prisma recto es (área de la base) × altura; el área superficial es la suma de las áreas de todas las caras. Elige la fórmula que corresponde a la figura.
Ejemplo 1: Un prisma rectangular recto mide 5 cm por 3 cm por 4 cm. Volumen = 5 × 3 × 4 = 60 cm³. Área superficial = 2(5×3 + 5×4 + 3×4) = 2(15 + 20 + 12) = 94 cm².
Ejemplo 2: Un prisma triangular tiene una base triangular de área 6 cm² y 10 cm de largo. Volumen = 6 × 10 = 60 cm³.
Ejemplo 3: El volumen se mide en unidades cúbicas y el área superficial en unidades cuadradas. Si la unidad de tu respuesta no coincide con la pregunta, la fórmula estaba mal.
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