Mathematics · Class 9
Surface Areas and Volumes
Surface areas and volumes of cubes, cuboids, cylinders, cones, and spheres.
3 sections15–25 min read6 MCQs · 2 examples
Chapter Overview
Surface Areas and Volumes in Class 9 covers formulas for cuboid, cube, right circular cylinder, cone, sphere, and hemisphere — total surface area, curved surface area, and volume.
Surface Areas
Cuboid TSA
2(lb + bh + hl)
Cube TSA
6a²
Cylinder CSA
2πrh
Cone CSA
πrl
Sphere SA
4πr²
Volumes
Cuboid
V = lbh
Cube
V = a³
Cylinder
V = πr²h
Cone
V = (1/3)πr²h
Sphere
V = (4/3)πr³
Solved Examples
Step-by-step solutions — read each step before checking the final answer.
Example 1: Cylinder volume
Find volume of cylinder with r = 7 cm, h = 10 cm.
- 1V = πr²h = π × 49 × 10
- 2V = 490π cm³ ≈ 1539.4 cm³
Answer
490π cm³
Example 2: Cube surface area
Edge of cube is 5 cm. Find total surface area.
- 1TSA = 6a² = 6 × 25
Answer
150 cm²
Key Points to Remember
- ✓ CSA excludes top and bottom for solids like cylinder
- ✓ Cone volume is ⅓ of cylinder with same base and height
- ✓ Use consistent units (cm, m)
Exam Tips
- • Write formula before substituting
- • Use π = 22/7 or 3.14 as instructed
- • Distinguish TSA from CSA in word problems
Practice MCQs — Surface Areas and Volumes
Test your understanding with topic-wise multiple choice questions. Explanations appear after each answer.
Question 1 of 6Score: 0/0
Volume of cube of edge a is: