Mensuration Class 10 Case Study Questions (CBSE New Pattern 2026)
The CBSE 2026 exam pattern focuses heavily on case study-based questions. Mensuration is one of the most scoring chapters if you understand how to apply formulas in real-life situations.
✔ Focus on real-life applications
✔ Multi-step problem solving
✔ Concept + calculation combined
📌 Important Mensuration Formulas
- Surface Area of Sphere = 4πr²
- Volume of Sphere = (4/3)πr³
- Volume of Cylinder = πr²h
- Volume of Cone = (1/3)πr²h
- Frustum Volume = (1/3)πh(R² + r² + Rr)
📊 Visual Understanding of Shapes
Sphere Representation
Cylinder Representation
Cone Representation
🧠 Case Study 1: Water Tank Problem
A cylindrical water tank has radius 3 m and height 7 m. It is filled with water. Water is transferred into small spherical containers of radius 0.5 m.
Questions:
- Find volume of tank
- Find volume of one sphere
- How many spheres can be filled?
Solution:
Volume of cylinder = πr²h = π × 3² × 7 = 63π
Volume of sphere = (4/3)π(0.5)³ = (4/3)π × 0.125 = 0.167π
Number of spheres = 63π / 0.167π ≈ 377
Final Answer: 377 spheres
Volume of cylinder = πr²h = π × 3² × 7 = 63π
Volume of sphere = (4/3)π(0.5)³ = (4/3)π × 0.125 = 0.167π
Number of spheres = 63π / 0.167π ≈ 377
Final Answer: 377 spheres
🧠 Case Study 2: Ice Cream Cone
An ice cream cone is filled with ice cream in the shape of hemisphere on top.
Radius = 3 cm, height = 9 cm
Volume = Cone + Hemisphere
Cone = (1/3)πr²h = (1/3)π × 9 × 9 = 27π
Hemisphere = (2/3)πr³ = (2/3)π × 27 = 18π
Total = 45π cm³
Cone = (1/3)πr²h = (1/3)π × 9 × 9 = 27π
Hemisphere = (2/3)πr³ = (2/3)π × 27 = 18π
Total = 45π cm³
🧠 Case Study 3: Metal Sphere Melting
A solid sphere is melted and recast into a cylinder of same radius.
Find height of cylinder.
Volume sphere = Volume cylinder
(4/3)πr³ = πr²h
h = 4r/3
(4/3)πr³ = πr²h
h = 4r/3
🧠 Case Study 4: Frustum Bucket
A bucket is shaped like a frustum with radii 7 cm and 14 cm, height 21 cm.
Volume = (1/3)πh(R² + r² + Rr)
= (1/3)π × 21 × (196 + 49 + 98)
= 7π × 343 = 2401π cm³
= (1/3)π × 21 × (196 + 49 + 98)
= 7π × 343 = 2401π cm³
🧠 Case Study 5: Pipe Flow Problem
Water flows through a cylindrical pipe of radius 7 cm at speed 10 cm/s.
Find volume per second.
Volume = πr²h
= π × 49 × 10 = 490π cm³/sec
= π × 49 × 10 = 490π cm³/sec
🎯 Exam Tips
- Always write formula first
- Convert units properly
- Use π = 22/7 unless specified
- Break complex shapes into simple ones