Chapter 11 · Class IX Mathematics · NCERT Exercises

Surface Areas and Volumes — Exercises

Cuboid · Cube · Cylinder · Cone · Sphere — All SAV Problems Solved

📂 1 Exercise 📝 9 Questions 🎓 Moderate

▶ Start Exercises 📖 Revise Notes

Exercise Index

①

Exercise 11.1

Surface area and volume of cuboid, cube, cylinder, right circular cone, sphere and hemisphere; word problems

9 Q Moderate

1 exercise file · 9 total questions

Chapter at a Glance

CBSE BoardsNTSE

12 Concepts

16 Formulas

Moderate Difficulty

10–12% Weightage

Before You Begin

Prerequisites

✓Area of rectangles and circles
✓Pythagoras theorem (for slant height)
✓Basic multiplication and squaring

Have Ready

🔧Formulae card for all 5 solids
🔧Calculator
🔧π = 22/7 unless stated otherwise

Exercise Topic Map

Exercise 11.1 Identify the solid from description; extract dimensions l,b,h or r,h; apply correct TSA/CSA and Volume formula; substitute and simplify; include π correctly

Key Formulae — Recall Before Solving

\(\text{Cuboid: }TSA=2(lb+bh+hl),\; V=lbh;\quad \text{Cube: }TSA=6a^2,\; V=a^3\)

\(\text{Cylinder: }CSA=2\pi rh,\; TSA=2\pi r(r+h),\; V=\pi r^2 h\)

\(\text{Cone: }l=\sqrt{r^2+h^2},\; CSA=\pi rl,\; TSA=\pi r(r+l),\; V=\tfrac{1}{3}\pi r^2 h\)

\(\text{Sphere: }SA=4\pi r^2,\; V=\tfrac{4}{3}\pi r^3;\quad \text{Hemisphere: }CSA=2\pi r^2,\; TSA=3\pi r^2,\; V=\tfrac{2}{3}\pi r^3\)

NCERT Solving Method

Step 1 — Read the question: identify the solid type (cuboid/cube/cylinder/cone/sphere/hemisphere). Step 2 — List the given dimensions clearly: r, h, l, a, l, b as applicable. Step 3 — For cone: always compute slant height l = √(r²+h²) FIRST before any other formula. Step 4 — TSA vs CSA: TSA includes all surfaces (closed); CSA excludes flat circular faces. Read the question to know which is needed. Step 5 — Volume problems: equate volumes when converting shapes (e.g., melting a sphere into cones); solve for unknown. Step 6 — Keep π as 22/7 until the final step; do not convert to decimal mid-calculation.