Geometry
GradesGrade 7GeometrySurface Area & Volume of Prisms and Pyramids

Surface Area & Volume of Prisms and Pyramids

📐 Geometry
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Surface Area & Volume of Prisms and Pyramids

Surface area covers the outside; volume fills the inside!

SURFACE AREA is the total area of all the faces of a 3D solid — how much material you need to cover it. VOLUME is the space inside the solid — how much it can hold. Both are essential in real-world design, packaging, and engineering.

Surface Area

Sum of areas of all facesMeasured in square units (cm², m²)Like how much wrapping paper covers a gift

Volume

Space enclosed inside the solidMeasured in cubic units (cm³, m³)Like how much water fills a tank

Surface area is 2D (faces); volume is 3D (inside space).

📦Rectangular prism: 6 cm × 4 cm × 3 cm
SURFACE AREA:
Top + Bottom: 2 × (6 × 4) = 48 cm²
Front + Back: 2 × (6 × 3) = 36 cm²
Left + Right: 2 × (4 × 3) = 24 cm²
Total SA = 48 + 36 + 24 = 108 cm²

VOLUME:
V = l × w × h = 6 × 4 × 3 = 72 cm³
Vprism=B⋅hVpyramid=13B⋅hV_{\text{prism}} = B \cdot h \qquad V_{\text{pyramid}} = \tfrac{1}{3} B \cdot h
🔺Volume of a square pyramid
Base area = 6 × 6 = 36 cm²
Height = 9 cm
V = (1/3) × 36 × 9 = (1/3) × 324 = 108 cm³

A pyramid holds exactly 1/3 the volume of a prism with the same base and height!
✏️ Try It!

A rectangular box is 5 cm long, 4 cm wide, and 3 cm tall. What is its volume?

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Remember This!

For surface area, "unfold" the solid into its net — then add up each flat face. Drawing a net prevents you from missing a face!

Practice with CalcVerse
📦Surface Area & Volume
Take Quiz 📝 — 25 Questions