3D Shapes (III): Cylinder & Cone
FoundationCylinder: 2 circular faces; cone: 1 circle + 1 apex.
After this lesson, you can:
- A cylinder: 2 equal circular faces + 1 curved surface
- A cone: 1 circular face + 1 curved surface + 1 apex
- Count circles: 2 means cylinder, 1 means cone
1Summary 重點摘要
Cylinder: 2 circular faces; cone: 1 circle + 1 apex.
2Vocabulary cards Vocabulary
c
cylinder圓柱
A solid with two equal circular faces, e.g. a can.
c
cone圓錐
A solid with one circular face and one apex, e.g. a traffic cone.
f
face面
A flat or curved surface of a solid.
c
curved surface曲面
A rounded surface, e.g. the side of a cylinder.
c
circular face圓面
A flat circle; a cylinder has two, a cone has one.
a
apex頂點／尖
The sharp point at the top of a cone.
e
edge稜／邊
The line where two faces meet, e.g. the rim of a cylinder.
r
roll滾動
Curved surfaces let solids roll, e.g. a can on its side.
3Step by step Steps
- Part 1: What a cylinder looks likeA cylinder looks like a can: the top and bottom faces are circles of the same size, and the side is a curved surface. Lay the can on its side and push it gently, and it rolls in a straight line. This is a special feature of cylinders.
- Part 2: What a cone looks likeA cone looks like an ice-cream cone: its base is a circle, the side is curved, and it narrows towards the top, ending in a sharp point called the apex. Count the flat faces: a cone has only one, the circle at the bottom.
- Part 3: Telling them apartTo tell them apart, count the circular faces. A can has 2 circular faces, one on top and one below; an ice-cream cone has only 1 circular face at the base, plus an apex. Two circles mean cylinder; one circle plus a point means cone.
- Part 4: Different rollingThey roll in different ways. A can on its side rolls in a straight line, while a cone rolls in a circle, because its flat face is not even all around. Standing upright on the table, neither of them rolls; both stay still.
- Part 5: Everyday examplesThere are many examples in daily life. Cylinders include cans, cups, glue bottles and paper-towel tubes; cones include ice-cream cones, party hats, traffic cones and funnels. When you see these objects, say their shape names in your head.
- Part 6: The cylinder and cone familyCylinders and cones belong to two big families. Prisms have two matching faces at the ends: a box ends in rectangles, a cylinder ends in circles. Cones and pyramids have one base plus an apex: a pyramid is square-based, and an ice-cream cone is a cone.
4Diagrams Diagrams
5Worked example Example
Example: a solid has 1 circular base, 1 curved side and 1 apex. What solid is it, and how many circular faces does it have?
- Count the circular faces first: this solid has only 1, which is the base.
- Count the points next: it has 1 apex, a sharp point at the top.
- Compare with a cylinder: a cylinder has 2 circular faces and no apex, so it does not match.
- Compare with a cone: 1 circular face plus 1 apex is an exact match.
- Answer: Answer: the solid is a cone, and it has 1 circular face. When telling solids apart, count the circular faces first and then look for an apex: two circles mean a cylinder, while one circle plus a sharp point means a cone.
6Common mistakes Mistakes
✗ Saying a cylinder has 1 circular face
✓ A cylinder has one circle on top and one below — 2 in total
✗ Mixing up a cone and a cylinder
✓ A cone has an apex, a cylinder does not; 1 circular face vs 2
✗ Saying a cylinder cannot roll
✓ On its side the curved surface lets it roll in a straight line
✗ Calling an ice-cream cone a triangular prism
✓ Its base is a circle, so it is a cone; prism faces are all flat
7Quick check Quick check
Q1What solid is a can?
Answer: A cylinder
Did you get it right?
Q2How many circular faces does a cone have?
Answer: 1
Did you get it right?
Q3How many circular faces does a cylinder have?
Answer: 2 (top and bottom)
Did you get it right?
Q4What is the sharp point on top of a cone called?
Answer: The apex
Did you get it right?
Q5Which solid matches a party hat?
Answer: A cone
Did you get it right?
8Recap Recap
- A cylinder: 2 equal circular faces + 1 curved surface
- A cone: 1 circular face + 1 curved surface + 1 apex
- Count circles: 2 means cylinder, 1 means cone
- A cylinder rolls straight; a cone rolls in a circle
- Cans and cups are cylinders; traffic cones and party hats are cones