Study guides › Level 7 · Geometry

Volumes: cylinders, cones and balls

Level 7 · Geometry · for questions like “A can has a radius of 3 cm and a height of 10 cm. What is its volume?”

💡 The idea

• Cylinder: πr² × height (the circle on the bottom, stacked up).
• Cone: ⅓ × πr² × height (a third of the cylinder).
• Ball (sphere): 4/3 × π × r³.

✏️ Worked examples

1. Can with radius 3, height 10: π × 9 × 10 = 90π cubic cm.

2. Cone with radius 3, height 10: a third of 90π = 30π.

3. Ball with radius 3: 4/3 × π × 27 = 36π.

⚠️ Watch out

• Radius, not diameter. Halve the diameter first.
• Square the radius for cylinders and cones, and cube it for balls.

🎯 Try these

1. Cylinder with radius 2, height 7
2. Cone with radius 6, height 5
3. Ball with radius 6

Answers: 1) 28π 2) 60π 3) 288π

This guide is also in the 10MathQ app: tap “📖 Study guide” after a question.