Solid shapes · Usually met around P5
Cross-sections of solids
Prisms: same as the base; pyramids and cones: smaller towards the top.
How to do it
Method
Prisms: same as the base; pyramids and cones: smaller towards the top
Cylinder cut across → the same circle
Another way
Slice by slice
A cone's circles shrink towards the point
In full
Cutting a solid with a flat plane makes a cross-section, the shape of the cut. Cut a prism or cylinder parallel to its base and every cross-section has the same shape and size as the base: a triangle for a triangular prism, a circle for a cylinder. Cut a pyramid or cone parallel to its base and the cross-section has the base's shape but gets smaller towards the top. A sphere cut any way gives a circle; through the centre it is biggest, with the sphere's diameter. Imagine slicing the solid thinly, or make one from modelling clay and cut it.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
A cone's base is 4 cm across. Cut parallel to the base, what happens to the circle the nearer the cut is to the point?
- A. The same, 4 cm across
- B. It gets bigger
- C. It becomes a triangle
- D. It gets smaller
Choose the right answer
Show the answer and working
Answer: D. It gets smaller
A cone's cross-sections are circles shrinking from the base to a point at the top.
Example 2
The solid in the picture is cut parallel to its base. Which shape is the cut (the cross-section)?
- A
- B
- C
- D
Choose the right picture
Show the answer and working
Answer: D
Cut parallel to the base, the cross-section has the base's shape.
Example 3
If the solid in the picture is sliced many times parallel to its base, every cross-section is the same size.
True or false?
Show the answer and working
Answer: True
Prisms and cylinders (cubes and cuboids too) have every slice the size of the base; pyramids and cones get smaller towards the top.
Practise it in the game →Solid shapes · Free to start, unlimited questions, no download