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.