Compare parallel slices through right prisms and pyramids.
Free examples and worked answers. No account needed.
Practise the method.
Compare parallel slices through right prisms and pyramids.
Compare parallel slices through right prisms and pyramids.
Example 1
Two slices are made at different positions inside a right rectangular prism. Both slicing planes are parallel to its rectangular bases. The first cross-section is 18cm by 7cm. What is the area of the second cross-section, in square centimetres?
Show worked answer
Answer: 126
Parallel sections through this prism have the same rectangular shape and size. The second section is also 18cm by 7cm.
Area =18×7=126 square centimetres.
Example 2
The two solids are a right square prism and a square pyramid. Each is cut parallel to its base at one-third and two-thirds of its height above the base. The table shows the side lengths of the square cross-sections. Which solid is the prism?
Parallel square cross-sections
Height above base
Solid A: side (cm)
Solid B: side (cm)
One-third of height
12
20
Two-thirds of height
6
20
Show worked answer
Answer: Solid B
The prism has parallel cross-sections of the same shape and size: square sides of 20cm at both heights.
The pyramid's square sides decrease from 12cm to 6cm toward its apex. The prism is therefore Solid B.
Example 3
A right prism has regular triangle-shaped bases. Each base has 3 equal sides of 3cm. A slice is made parallel to the bases, strictly inside the prism. Which shape and perimeter describe the cross-section?
Right prismDiagram not to scaleShow worked answer
Answer: triangle; perimeter 9cm
A parallel section has the same shape and size as a base: a triangle with 3 sides of 3cm.
Its perimeter is 3×3=9cm.
Put it into practice.
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