3D Shapes & Volume
Year 8 📐 Geometry & Measures Identify 3D shapes, calculate volume and surface area.
📦 Surface Area
Surface area is the total area of all faces of a 3D shape. Add the area of every face.
⚡ Cuboid Surface Area
$$SA = 2(lw + lh + wh)$$⚡ Cylinder Surface Area
$$SA = 2\pi r^2 + 2\pi r h$$Example: Cuboid $4 \times 3 \times 2$ cm: $SA = 2(12+8+6) = 52$ cm²
🧊 Volume of Prisms and Cylinders
Volume measures the 3D space inside a shape. Units are always cubed (cm³, m³, etc).
⚡ Prism Volume
$$V = \text{cross-sectional area} \times \text{length}$$⚡ Cylinder Volume
$$V = \pi r^2 h$$Example: Cylinder with $r=5$ cm, $h=10$ cm: $V = \pi \times 25 \times 10 = 250\pi \approx 785.4$ cm³
🌍 Pyramids, Cones and Spheres
Pointy and curved shapes use a factor of $\frac{1}{3}$ or $\frac{4}{3}$ in their volume formulas.
⚡ Pyramid and Cone
$$V = \frac{1}{3} \times \text{base area} \times h$$⚡ Sphere
$$V = \frac{4}{3}\pi r^3 \qquad SA = 4\pi r^2$$Example: Sphere with $r=6$ cm: $V = \frac{4}{3}\pi(216) = 288\pi \approx 904.8$ cm³
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