📦🔢 Mastering Volume & Surface Area of 3-D Shapes!

Ever wondered how much water a tank holds or how much wrapping paper you need for a gift box? **Volume** tells us the space inside a 3-D shape, while **surface area** measures all the faces we can touch. These skills pop up in exam questions, real-life packing, and science experiments—so mastering them is a must for every O-Level student!

Key Concepts & Formulas

Cuboid: Volume $V = l\times b\times h$ , Surface Area $SA = 2(lb + bh + hl)$
Cylinder: Volume $V = \pi r^{2}h$ , Curved Surface Area $CSA = 2\pi rh$ , Total $SA = 2\pi r(r+h)$
Right Prism (any cross-section): Volume $V = \text{Area of cross-section} \times \text{length}$ , Surface Area = Sum of areas of all faces

Worked Example: Holiday Gift Box

Problem: A cuboid gift box measures 8\,cm by 5\,cm by 3\,cm. Find (a) its volume, (b) its total surface area. Solution:
1. **Volume**:

V = 8 \times 5 \times 3 = 120\,\text{cm}^3

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2. **Surface Area**:

SA = 2(8\times5 + 5\times3 + 3\times8) = 2(40 + 15 + 24) = 2 \times 79 = 158\,\text{cm}^2

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Always label units and double-check each face is counted!