Quantitative Aptitude
Mensuration for exams
Areas and volumes of common shapes, with exam-style shortcuts.
Rectangle area = l × b; circle area = πr²; circumference = 2πr.
Cuboid volume = l × b × h; cylinder = πr²h; cone = ⅓πr²h; sphere = ⁴⁄₃πr³.
Use π = 22/7 when the radius is a multiple of 7.
📌 Remember for the exam
- Choose π = 22/7 for multiples of 7
- If all lengths scale by k, area scales by k² and volume by k³
🎯 Learning objective: Calculate volume and surface area of cubes, cylinders, cones and spheres.
💬 Questions and answers
1What am I looking at?
Answer: A solid shape that you can resize.
2What are its parts? (click a part to identify it)
Answer: Radius, height or side, faces and curved surfaces.
3How does it work?
Answer: Volume measures the space inside (cubic units); surface area measures the outer covering (square units).
4Why is it important?
Answer: Used for tanks, cans, rooms, packaging and construction.
5What happens if I change something? (use the sliders)
Answer: Double the radius of a cylinder and see the volume become four times larger.
6What should I remember for the exam?
Answer: Cube a³ and 6a²; cylinder πr²h and 2πr(r + h); cone ⅓πr²h; sphere ⁴⁄₃πr³ and 4πr².