Cross Sections of Solids
A cross section is the 2D shape we get when cutting straight through a 3D object. For example, the orange below (let's pretend it's a perfect sphere) has been cut along the vertical plane (straight up an down). The cross section of the orange, where we can see inside, is a circle.
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3D shapes have more than one cross section and they may or not be the same shape, depending on which way you cut them. For example, look at the cylinder below. If we cut it along the horizontal plane, the cross section is a circle. However, if we cut it along the vertical plane, the cross section is a rectangle.
Since prisms have more than one cross section, it's important to consider all possibilities when we're asked to match a cross section with a 3D shape. For example, we saw that a rectangle could be a cross section of a cylinder. However it could also be the cross section of a rectangular prism or even a triangular prism!
Worked Examples
Question 1
Which of these shows the cross section of a prism?
Question 2
The cylinder shown consists of two circular faces. Which of the following shows a cross section of the cylinder?
Question 3
If the cross section of a solid is shown to the right, what could the solid be? Select all the correct options.