📚 Concepts

📚 Surface Area

• The total area that the surface of a 3D object occupies. It includes all outer faces.

📚 Curved Surface Area (CSA)

• The area of only the curved part (excluding base or top). E.g., side of a cylinder.

📚 Total Surface Area (TSA)

• Sum of all outer surfaces – includes curved and flat parts (base/top).

📚 Volume

• The amount of space enclosed by a 3D object. Measured in cubic units (e.g., cm³, m³).

📚 Cube

• A 3D solid with all edges equal and all faces as squares.

📚 Cuboid

• Like a box – 6 rectangular faces, with possibly different length, breadth, and height.

📚 Cylinder

• Has two equal circular bases and one curved surface joining them.

📚 Cone

• Has a circular base and a curved surface that tapers to a point (vertex).

📚 Sphere

• A perfectly round 3D object – like a ball – with no flat surfaces or edges.

📚 Hemisphere

• Half of a sphere – has one curved surface and one circular base.

📚 Frustum of a Cone

• A cone with its top portion cut off parallel to its base. Has two circular ends of different radii.

📚 Slant Height (𝑙)

• Used in cones and frustums – the distance along the side from base to tip (or upper circle).

✍️ Formulas

🧊 Cube

• Total Surface Area (TSA) = 6𝐚²

• Volume (V) = 𝐚³

📦 Cuboid

• Total Surface Area (TSA) = 2(𝐥𝐛 + 𝐛𝐡 + 𝐥𝐡)

• Volume (V) = 𝐥 × 𝐛 × 𝐡

🥫 Cylinder

• Curved Surface Area (CSA) = 2π𝐫𝐡

• Total Surface Area (TSA) = 2π𝐫(𝐡 + 𝐫)

• Volume (V) = π𝐫²𝐡

🍦 Cone

• Curved Surface Area (CSA) = π𝐫𝐥

• Total Surface Area (TSA) = π𝐫(𝐥 + 𝐫)

• Volume (V) = (1/3)π𝐫²𝐡

⚽ Sphere

• Total Surface Area (TSA) = 4π𝐫²

• Volume (V) = (4/3)π𝐫³

🌗 Hemisphere

• Curved Surface Area (CSA) = 2π𝐫²

• Total Surface Area (TSA) = 3π𝐫²

• Volume (V) = (2/3)π𝐫³

🔺 Frustum of a Cone

• Curved Surface Area (CSA) = π(𝐫₁ + 𝐫₂)𝐥

• Total Surface Area (TSA) = π(𝐫₁ + 𝐫₂)𝐥 + π𝐫₁² + π𝐫₂²

• Volume (V) = (1/3)π𝐡(𝐫₁² + 𝐫₂² + 𝐫₁𝐫₂)