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Volume & Surface Areas

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Quantitative Aptitude - Volume & Surface Areas

1. Volume Formulas

  • Cuboid: \( lwh \); Cube: \( a^3 \)
  • Cylinder: \( \pi r^2 h \); Sphere: \( \frac{4}{3} \pi r^3 \)
  • Cone: \( \frac{1}{3} \pi r^2 h \); Hemisphere: \( \frac{2}{3} \pi r^3 \)

2. Surface Area Formulas

  • Cuboid total: \( 2(lw + lh + wh) \)
  • Cube: \( 6a^2 \)
  • Cylinder total: \( 2\pi r (r + h) \)
  • Sphere: \( 4\pi r^2 \); Hemisphere: \( 3\pi r^2 \)
  • Cone: \( \pi r (r + l) \), where l = slant height.

3. Quick Tips

  • Always match units (cm³, m²).
  • Simplify using \( \pi ≈ 22/7 \) when divisible.

4. Mistakes to Avoid

  • Mixing radius with diameter.
  • Using volume formulas for surface area problems.

5. Revision Checklist

  • Memorize volume and surface area formulas.
  • Practice conversion between units (cm³ to m³).

Summary: Use correct formula set, check units, factor π appropriately, and break composite solids into parts if needed.

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