Surface Area & Volume of Solids

By Class VIII the child moves from flat figures to solids, and a new misconception appears: confusing surface area (how much skin a solid has, measured in square units) with volume (how much space it fills, measured in cubic units). Surface area is what you would paint or wrap; volume is what you would fill with water or sand. For a cuboid of length l, breadth b and height h: volume = l × b × h and total surface area = 2(lb + bh + hl). A cube is the special case where l = b = h = a, so volume = a³ and total surface area = 6a² (six identical square faces). For a cylinder of radius r and height h: volume = πr²h, curved (lateral) surface area = 2πrh, and total surface area = 2πr(r + h). CTET likes to test the unit jump — a tank holding water is a volume question (m³ or litres, where 1 m³ = 1000 litres), while wrapping or painting a box is a surface-area question (m²). A good teacher introduces volume with unit cubes (how many 1 cm cubes fill the box?) so the formula l × b × h is felt as a count of cubes, not a memorised string. Watch the doubling trap again: doubling every edge of a cube multiplies the volume by 2³ = 8 and the surface area by 2² = 4.

✅ Solved examples

✏️ Practice — try these, take hints as needed

📝 Topic test — 8 questions

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