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Cross-sections of solids
Recognition and area problems for sections of cubes, prisms, pyramids, cylinders and cones.
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The vertices of the cross-section are the midpoints of the three cube edges meeting at one vertex. Each side of the cross-section is a midline in a triangular half of a cube face, so its length is a/√2. The cross-section is an equilateral triangle. Calculate its area using S = s²√3/4.
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Question 10out of 10
The vertices of the cross-section are the midpoints of the three cube edges meeting at one vertex. Each side of the cross-section is a midline in a triangular half of a cube face, so its length is a/√2. The cross-section is an equilateral triangle. Calculate its area using S = s²√3/4.
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Sample questions
- A plane passes through the midpoints of the three edges of a cube that meet at the same vertex. Calculate the area of the cross-section.
- A right prism has base ___ cm × ___ cm and height ___ cm. Find its diagonal-section area.
- A pyramid diagonal section has base ___ cm and height ___ cm. Find its area.
- What shape results when a cylinder is cut by a plane through its axis?
- What shape is an axial section of a right cone?
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