A focused Grade 7 learning session for Cross-Sections of Three-Dimensional Figures using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving cross-sections of three-dimensional figures.
Cross-Sections of Three-Dimensional Figures is part of Grade 7 Geometry and Scale. This activity focuses on the central idea students need before they move into independent practice.
Students will build Grade 7 mastery of cross-sections of three-dimensional figures using models, equations, and test-style reasoning.
| What to notice | How to use it |
|---|---|
| Numbers, units, labels, diagrams, or graphs | Identify what each part represents before calculating. |
| The relationship in the problem | Connect the model to an equation, comparison, or explanation. |
Use the figures and worked questions in the practice set below as the visual model for this skill.
Read the first practice question slowly. Decide what the question is asking, choose a strategy, solve, and then compare your reasoning with the answer explanation.
For Cross-Sections of Three-Dimensional Figures, a strong worked example should show the setup, the calculation or model, and a final answer that matches the context.
Many Grade 7 test questions use real situations. Look for quantities, units, rates, measures, expressions, or data values that connect the math to the story.
After solving, explain what the answer means in the situation, not just the number you calculated.
I can solve problems involving cross-sections of three-dimensional figures.
Use the warmup, guided question, practice set, and exit questions below to check whether this skill is ready or needs more practice.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
What is the shape of the cross-section formed when a cube is sliced parallel to one of its faces?
Answer C: Square
A cube has all square faces. A cut parallel to any face produces a square cross-section congruent to that face.
A rectangular prism has dimensions \(4\text{ cm} \times 6\text{ cm} \times 8\text{ cm}\). If a vertical plane cuts through it perpendicular to the base, which shape MUST appear in the cross-section?
Answer B: Rectangle
Any vertical plane perpendicular to the base of a rectangular prism intersects the solid in a rectangular cross-section (width is one base dimension, height is the prism height).
A plane cuts diagonally through the cube as shown. What is the shape of the resulting cross-section?
Answer A: Rectangle
A plane through opposite edges of a cube forms a rectangular cross-section. One pair of sides equals the edge length; the other pair equals the face diagonal (\(a\sqrt{2}\) for edge \(a\)).
When a cylinder is cut by a horizontal plane parallel to its circular bases, what is the shape of the cross-section?
Answer C: Circle
A horizontal plane parallel to the bases of a cylinder creates a circular cross-section congruent to the bases. The radius of this circle equals the radius of the cylinder.
A cylinder is sliced by an oblique plane, as shown. What is the shape of the resulting cross-section?
Answer C: Ellipse
When a plane cuts through a cylinder at an angle (not parallel to the bases and not perpendicular to the axis), the cross-section is an ellipse.
Which of the following statements is true about cross-sections of a cube?
Answer B: A cross-section can be a triangle, rectangle, or hexagon
Depending on the angle and position of the cutting plane, a cube's cross-section may have 3, 4, 5, or 6 sides. A triangle results from a corner cut; rectangles from parallel cuts; hexagons from diagonal cuts at certain angles.
A cone is sliced horizontally (parallel to its circular base). What is the shape of the cross-section?
Answer C: Circle
A horizontal plane parallel to the base of a cone produces a circular cross-section smaller than the original base. The circle is similar to the base but scaled down based on the height of the cut.
A cone is cut by a plane perpendicular to its axis, as shown. What is the shape of the resulting cross-section?
Answer C: Circle
Any plane perpendicular to a cone's axis creates a circular cross-section. The smaller the radius of the cross-section, the higher up on the cone the cut is made.
A pyramid with a square base is sliced parallel to its base. Which statement about the cross-section is correct?
Answer B: The cross-section is a square, smaller than the base
A square pyramid cut parallel to its base produces a square cross-section. This square is similar to the base but smaller in size, with the side length proportional to the distance from the apex.
A square pyramid is cut by a plane parallel to its base. The cross-section is a square. If the pyramid has a height of 12 cm and the cut is made 4 cm from the apex, how does the area of the cross-section compare to the base?
Answer B: It is \(\frac{1}{9}\) of the base area
The ratio of areas equals the square of the ratio of corresponding lengths. The cut is at height 4 cm out of 12 cm, so the ratio is \(\frac{4}{12} = \frac{1}{3}\). Squaring: \((\frac{1}{3})^2 = \frac{1}{9}\).
A rectangular prism with dimensions \(5\text{ cm} \times 7\text{ cm} \times 10\text{ cm}\) is cut by a plane parallel to the base. The cross-section is a rectangle with area \(35\text{ cm}^2\). Which dimension of the prism determines the area of the cross-section?
Answer B: The base dimensions (\(5\text{ cm} \times 7\text{ cm}\))
A plane parallel to the base always produces a cross-section congruent to the base. The cross-section's area is \(5 \times 7 = 35\text{ cm}^2\), independent of the prism's height.
