GCSE · Geometry and measures

Cross-sections of solids

Slide a horizontal cut through a prism, cylinder, cone or sphere.

Choose Cone, then compare cuts at 25%, 50% and 75% of the height.

A=\pi r_{\text{section}}^2

Scroll the diagram sideways to see every label.

Slices shrink towards the apex.

Cut above the base: 4 cm
Section radius: 2 cm
Section area: 12.566 cm²

The cut is horizontal and parallel to the base (or equator for the sphere). At a cone apex or sphere pole, the circle shrinks to a point. This model explores only horizontal cuts.

Predict, test and explain

Step 1 of 3

Predict

Are all horizontal slices of a cone the same size?

Explore and compare

Choose the investigation above. Predict what will change before you move a control.

Predict

Try it in the simulation. Change one thing at a time.

Explain

Notes and saved values stay in this tab. They disappear when you reload.

Hints, self-check and connections

Try a self-check

Fixed values, separate from the diagram controls.

Are all horizontal slices of a cone the same size?

Hint

Parallel slices of a cone are similar circles; their radii decrease linearly with height.

Reveal answer

Parallel slices of a cone are similar circles; their radii decrease linearly with height.

Build an explanation

Hint 1

Parallel slices of a cone are similar circles; their radii decrease linearly with height.

Hint 2

Use the labels and units in the live model to check your method.

Hint 3

Explain which lengths, areas or volumes are being compared.

Worked example

This example uses fixed values, separate from the diagram controls.

A sphere has radius 5 cm. A plane is 3 cm above its centre. Find the cross-section radius and area.

Draw a right triangle from the sphere centre to the cut circle.
Section radius² = 5² − 3² = 16.
Use the positive radius, then calculate π × 4².

Answer: Radius 4 cm; area 16π cm².

Connect this idea

Watch out: Parallel slices of a cone are similar circles; their radii decrease linearly with height.