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Cross-sections of solids
Recognition and area problems for sections of cubes, prisms, pyramids, cylinders and cones.
Questions: 10Estimated time: 20 minutes
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Question 1out of 10
What shape results when a cylinder is cut by a plane through its axis?
A cylinder axial section is a rectangle with sides 2r and h. Its area is 2rh. Use the diameter, not just the radius.
Question 2out of 10
What should first be identified before calculating a section area?
A section is the intersection of a solid with a plane. Identify its shape and dimensions before calculating. An axial section plane passes through the rotation axis; section area is not the total surface area.
Question 3out of 10
A right prism has base 3 cm × 4 cm and height 7 cm. Find its diagonal-section area.
The diagonal section of a right prism is a rectangle. Its width is the base diagonal √(a² + b²) and height h. Section area = h√(a² + b²).
Question 4out of 10
What shape is an axial section of a right cone?
A cone axial section is an isosceles triangle with base 2r. A triangular pyramid section has area base × perpendicular section height / 2. Use the section dimensions rather than those of a different face.
Question 5out of 10
A plane passes through the midpoints of the three edges of a cube that meet at the same vertex. The edge of the cube is 12 cm. Find the area of the cross-section.
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.
Question 6out of 10
A plane passes through the midpoints of the three edges of a cube that meet at the same vertex. The edge of the cube is 12 cm. Find the area of the cross-section.
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.
Question 7out of 10
A right prism has base 32 cm × 60 cm and height 2 cm. Find its diagonal-section area.
The diagonal section of a right prism is a rectangle. Its width is the base diagonal √(a² + b²) and height h. Section area = h√(a² + b²).
Question 8out of 10
A pyramid diagonal section has base 24 cm and height 9 cm. Find its area.
A cone axial section is an isosceles triangle with base 2r. A triangular pyramid section has area base × perpendicular section height / 2. Use the section dimensions rather than those of a different face.
Question 9out of 10
What does “axial section” mean?
A section is the intersection of a solid with a plane. Identify its shape and dimensions before calculating. An axial section plane passes through the rotation axis; section area is not the total surface area.
Question 10out of 10
A sphere is cut through its centre. The section-circle radius is 4 cm. Find the area of its circumscribed square.
A square circumscribed about the circular section has side length 2r. Its area is S = (2r)² = 4r².
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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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