Cross-Section Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
A cylinder of radius 55 cm and height 1212 cm is cut by a horizontal plane halfway up its height. Describe and find the area of the cross-section.

Solution

  1. 1
    Step 1: A horizontal plane cuts perpendicular to the axis of the cylinder.
  2. 2
    Step 2: The cross-section is a circle with the same radius as the cylinder: r=5r = 5 cm.
  3. 3
    Step 3: Area =ฯ€r2=ฯ€(5)2=25ฯ€โ‰ˆ78.5= \pi r^2 = \pi (5)^2 = 25\pi \approx 78.5 cm2^2.

Answer

The cross-section is a circle; area =25ฯ€โ‰ˆ78.5= 25\pi \approx 78.5 cm2^2.
Any plane perpendicular to the axis of a cylinder produces a circular cross-section identical to the base. The height at which the cut occurs does not affect the shape or size, since the cylinder has constant cross-section along its axis.

About Cross-Section

The two-dimensional shape that is revealed when a three-dimensional solid is sliced through by a flat plane.

Learn more about Cross-Section โ†’

More Cross-Section Examples

Example 2 medium

A square pyramid with a [formula] cm [formula] [formula] cm base and height [formula] cm is cut by a

Example 3 medium

A cone is cut by a plane parallel to its base. What shape is the cross-section?

Example 4 easy

What shape is the cross-section when a sphere is cut by any plane through its centre? What is the ar

Example 5 hard

A cone with base radius [formula] cm and height [formula] cm is cut by a plane parallel to the base

โ† All Cross-Section Examples Cross-Section Concept