Cross section — Grade 7 Accelerated, what it means and where it is taught

The 2-D face revealed when a plane cuts through a solid.

Taught in Grade 7 Accelerated.

Where it is taught

What uses it later

This idea is needed for:

Practise this idea

10 questions in the course bank use Cross section, in Plane Sections of 3-D Figures, Solids: Volume, Sections & Rotations. The first 8 are below; the rest are in those units.

Problem 1

A cube is sliced parallel to one of its faces. What shape is the cross section?

  1. A square
  2. A triangle
  3. A circle
  4. A hexagon
Worked answer

A square

You get a square identical to the face, no matter how deep you cut.

Problem 2

A cylinder is sliced parallel to its base. What shape is the cross section?

  1. A rectangle
  2. A circle
  3. An oval
  4. A triangle
Worked answer

A circle

A circle, the same size as the base.

Problem 3

A square pyramid is sliced parallel to its base. What shape is the cross section?

  1. A triangle
  2. A square
  3. A trapezoid
  4. A pentagon
Worked answer

A square

A square — smaller the higher up you cut.

Problem 4

What is the greatest number of sides a cross section of a cube can have?

Worked answer

6

A cube has 6 faces

A plane can be tilted to pass through all six at once

That gives a hexagon — 6 sides.

Problem 5

A cylinder has radius 4 cm and height 10 cm. It is cut vertically through its axis. Find the area of the cross section.

Worked answer

80

Height = 10 cm

Width = 2 × 4 = 8 cm

Area = 10 × 8 = 80 cm2

Problem 6

A cone is sliced parallel to its base. What shape is the cross section?

  1. A triangle
  2. A circle
  3. A trapezoid
  4. An oval
Worked answer

A circle

A circle — smaller the closer you cut to the tip.

Problem 7

A cube is sliced through the diagonal of its top face and the parallel diagonal of its bottom face. What shape is the cross section?

  1. A square
  2. A rectangle
  3. A triangle
  4. A hexagon
Worked answer

A rectangle

The plane crosses four faces, so the cross section has four sides

All four corners are right angles, but the horizontal sides are diagonals — longer than the vertical edges

So it is a rectangle, not a square.

Problem 8

A cube is sliced through the three vertices next to one corner. What kind of triangle appears?

  1. A right triangle
  2. An equilateral triangle
  3. A scalene triangle
Worked answer

An equilateral triangle

Each of the three sides is a diagonal of a square face

All the faces are identical, so all three diagonals are equal

The cross section is an equilateral triangle.

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