Understanding 3D Shapes: Cylinder, Cone, Sphere, and Ball
In this lesson, we'll explore four important three-dimensional (3D) shapes that you encounter every day. These shapes have curved surfaces, making them different from shapes like cubes and prisms.
The Cylinder
A cylinder is a 3D shape with:
- 1Two parallel circular bases (top and bottom)
- 2One curved surface connecting the bases
- 3The same radius throughout its height
Real-life examples: Cans, pipes, batteries, candles, drinking glasses
Key Formulas:
Volume: V = πr²h
Curved Surface Area: CSA = 2πrh
Total Surface Area: TSA = 2πr² + 2πrh = 2πr(r + h)
Where r = radius, h = height, π ≈ 3.14159
Interactive 3D Cylinder
Interactive visualization — available in the full lesson
The Cone
A cone is a 3D shape with:
- 1One circular base
- 2One curved surface that tapers to a point (apex)
- 3A slant height (l) from base edge to apex
Real-life examples: Ice cream cones, party hats, traffic cones, funnels
Key Formulas:
Volume: V = ⅓πr²h
Slant Height: l = √(r² + h²)
Curved Surface Area: CSA = πrl
Total Surface Area: TSA = πr² + πrl = πr(r + l)
Interactive 3D Cone
Interactive visualization — available in the full lesson