Mathematics
Grade 10
15 min
Cross-sections of three-dimensional figures
Cross-sections of three-dimensional figures
What you'll learn
- Identify unit fractions from a set of fractions with 100% accuracy.
- Solve 8 out of 10 multiplication problems involving a whole number and a unit fraction using visual models (e.g., number lines, area models).
- Explain, in writing, the process of multiplying a whole number by a unit fraction, using mathematical vocabulary (numerator, denominator, product) in at least 2 sentences.
- Apply the concept of multiplying a whole number by a unit fraction to solve 3 out of 4 real-world word problems correctly.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify the two-dimensional shape created by the intersection of a plane and a three-dimensional figure.
Describe how the angle and location of a slicing plane affect the shape and size of the resulting cross-section.
Visualize and sketch the cross-sections of common solids like prisms, pyramids, cylinders, cones, and spheres.
Calculate the area of a cross-section parallel to the base of a prism, cylinder, pyramid, or cone.
Differentiate between horizontal, vertical, and oblique (angled) cross-sections.
Apply the properties of similar figures to find the dimensions of cross-sections in pyramids and cones.
Ever wonder how a CT scanner sees inside the human body or how a chef cuts a carrot into perfect circles? 🥕 You're already thinking about cross-s...
2
Key Concepts & Vocabulary
TermDefinitionExample
Three-Dimensional Figure (Solid)An object that has three dimensions: length, width, and height. It occupies space.A cube, a sphere, a pyramid, or a cylinder.
PlaneA flat, two-dimensional surface that extends infinitely in all directions. In this context, we think of it as a 'slicing' tool.The surface of a table, a wall, or a sheet of paper can be thought of as parts of a plane.
Cross-SectionThe two-dimensional shape that is exposed when a plane intersects a three-dimensional figure.Slicing a cylindrical sausage horizontally results in a circular cross-section.
Horizontal Cross-SectionA cross-section created by a plane that is parallel to the base of the 3D figure.A horizontal slice through a square pyramid creates a smaller square.
Vertical Cross-SectionA c...
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Core Formulas
Prism/Cylinder Parallel Slice Rule
A cross-section created by a plane parallel to the base of a prism or a cylinder is congruent to the base.
Use this rule when a slice is made parallel to the top or bottom of a prism or cylinder. The area of the cross-section will be identical to the area of the base.
Pyramid/Cone Parallel Slice Rule
A cross-section created by a plane parallel to the base of a pyramid or a cone is a shape that is similar to the base, but smaller.
Use this rule for slices parallel to the base of a pyramid or cone. The cross-section will be a scaled-down version of the base. You will often need to use properties of similar triangles to find its dimensions.
Similar Figures Proportionality
For a cone or pyramid, the ratio of the linear dimensions of the c...
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Challenging
A plane slices a cube in such a way that it passes through the midpoints of 6 of its edges. The resulting cross-section is a regular hexagon. If the edge length of the cube is 8 cm, what is the perimeter of the hexagon?
A.24 cm
B.24√2 cm
C.48 cm
D.48√2 cm
Challenging
A horizontal cross-section of a pyramid has an area that is 1/9th of the area of the base. The total height of the pyramid is H. At what distance from the vertex was the slice made?
A.H/9
B.H/3
C.2H/3
D.H/81
Challenging
A right circular cylinder has a radius of 5 cm and a height of 20 cm. What is the maximum possible area of a rectangular cross-section?
A.100 cm²
B.200 cm²
C.25π cm²
D.500 cm²
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Frequently asked questions
What grade level is "Cross-sections of three-dimensional figures"?
Cross-sections of three-dimensional figures is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Cross-sections of three-dimensional figures?
You'll be able to: Identify unit fractions from a set of fractions with 100% accuracy; Solve 8 out of 10 multiplication problems involving a whole number and a unit fraction using visual models (e.g., number lines, area models); Explain, in….
Is "Cross-sections of three-dimensional figures" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Cross-sections of three-dimensional figures?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.