3D Shapes (II): Prisms & Cylinders
FoundationPrisms have two polygon bases; cylinders have two circular bases.
After this lesson, you can:
- Prisms: two equal polygon bases.
- A triangular prism has 5 faces.
- Cylinder: 2 circle bases + curved side.
1Summary 重點摘要
Prisms have two polygon bases; cylinders have two circular bases.
2Vocabulary cards Vocabulary
P
Prism角柱
Two equal polygon bases with rectangular sides.
T
Triangular prism三角柱
A prism with triangle bases.
R
Rectangular prism (cuboid)四角柱（長方體）
A prism with 4-sided bases.
C
Cylinder圓柱
Two circular bases and a curved side.
B
Base底面
The top and bottom faces.
C
Curved surface曲面
A bending face, not flat.
P
Pyramid角錐
Polygon base with triangle sides, like the pyramids.
F
Face面
A flat surface of a solid.
3Step by step Steps
- Step 1: Look at the basesWhen studying a 3D shape, look at its bases first. For example, pick up a triangular prism: you will see that its top and bottom are two triangles of the same size. What shape the bases are is an important clue for sorting solids, so look at them carefully.
- Step 2: Prism featuresA prism has two bases of the same shape and size, and its sides are rectangles. A triangular prism, for example, has 2 triangle bases plus 3 rectangular sides, making 2 + 3 = 5 faces in all. Counting the faces helps us recognise a prism.
- Step 3: Rectangular prismsA shoebox is a common quadrilateral prism, also called a rectangular prism, named after its four-sided base. Its top and bottom bases are rectangles and its four sides are rectangles too: 6 faces in all. Many dictionaries and bricks around us are quadrilateral prisms.
- Step 4: CylinderA cylinder has two circular bases of the same size, top and bottom, and one curved side. A food can, for example, stands steadily on a table. A cylinder has no corners and no sharp point, which is the biggest difference from a prism; lay it on its side and push gently, and it rolls.
- Step 5: PyramidThe pyramids are common square pyramids: 1 four-sided base at the bottom, 4 triangular sides around it, and all the faces meeting at one sharp point at the top. A pyramid differs from a prism: it has only one base, plus an apex.
- Step 6: Prism vs cylinderThe key to sorting is the base: if the base is a polygon with sides and corners, it is a prism; if the base is a circle, it is a cylinder. Look at the base first, then count the sides, and solids can be sorted clearly. Practise with a few objects and you will soon sort them quickly and correctly.
4Diagrams Diagrams
5Worked example Example
Example: a box has a triangle on the top and on the bottom, with rectangular sides. What solid is it? How many faces does it have?
- Look at the bases first: the top and bottom are 2 identical triangles, the same shape and size.
- The bases are polygons with sides and corners, so the solid is a prism; with triangle bases it is a triangular prism.
- Then count the sides: there are 3 rectangles, counting each face once without missing or repeating any.
- Finally add the faces: 2 + 3 = 5; two bases plus three sides make 5 faces in all.
- Answer: The box is a triangular prism with 5 faces. It has 2 identical triangle bases and 3 rectangular sides, and 2 + 3 = 5; because its bases are polygons with sides and corners, it matches the features of a prism.
6Common mistakes Mistakes
✗ Mixing cylinder and sphere
✓ A cylinder has 2 flat round bases and stands; a sphere is all curved and rolls
✗ Mixing prism and pyramid
✓ A prism has two bases; a pyramid has one base and a point on top
✗ Forgetting side faces of a triangular prism
✓ 2 bases + 3 sides = 5 faces
✗ Calling a cylinder's side a rectangle
✓ The side is curved; it only looks like a rectangle unrolled
7Quick check Quick check
Q1How many faces does a triangular prism have?
Answer: 5
Did you get it right?
Q2A can is what solid?
Answer: Cylinder
Did you get it right?
Q3The pyramids are prisms or pyramids?
Answer: Pyramids
Did you get it right?
Q4How many flat faces does a cylinder have?
Answer: 2
Did you get it right?
Q5What shape are a prism's side faces?
Answer: Rectangles
Did you get it right?
8Recap Recap
- Prisms: two equal polygon bases.
- A triangular prism has 5 faces.
- Cylinder: 2 circle bases + curved side.
- Pyramids have a point on top.
- Look at the bases to tell prism from cylinder.