Cross-Section Math Example 4

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

Example 4

easy
What 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 77 cm?

Solution

  1. 1
    Step 1: A plane through the centre of a sphere produces a cross-section called a great circle โ€” a circle with the same radius as the sphere.
  2. 2
    Step 2: Area =ฯ€r2=ฯ€(7)2=49ฯ€โ‰ˆ153.9= \pi r^2 = \pi (7)^2 = 49\pi \approx 153.9 cm2^2.

Answer

Circle (great circle); area =49ฯ€โ‰ˆ153.9= 49\pi \approx 153.9 cm2^2.
Any plane through the centre of a sphere cuts it along a great circle, which has the maximum possible area for a cross-section of that sphere. Planes not through the centre produce smaller circles.

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 1 easy

A cylinder of radius [formula] cm and height [formula] cm is cut by a horizontal plane halfway up it

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 5 hard

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

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