Practice Cross-Section in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The two-dimensional shape that is revealed when a three-dimensional solid is sliced through by a flat plane.
Slice an orange—the cut surface is a cross-section (a circle).
Example 1
easyA cylinder of radius 5 cm and height 12 cm is cut by a horizontal plane halfway up its height. Describe and find the area of the cross-section.
Example 2
mediumA square pyramid with a 6 cm \times 6 cm base and height 9 cm is cut by a horizontal plane 3 cm above the base. Find the shape and dimensions of the cross-section.
Example 3
mediumA cone is cut by a plane parallel to its base. What shape is the cross-section?
Example 4
easyWhat shape is the cross-section when a sphere is cut by any plane through its centre? What is the area if the sphere has radius 7 cm?
Example 5
hardA cone with base radius 6 cm and height 12 cm is cut by a plane parallel to the base at height 8 cm from the base. Find the radius and area of the cross-section, then compute the ratio of areas (cross-section : base).