Questions and Answers
Polyhedra with two faces that are congruent and parallel are prisms.
True
What is the doughnut-shaped, three-dimensional figure commonly called?
torus
The faces of a polyhedron are curved.
False
What is a pattern of two-dimensional figures that can be folded into a three-dimensional figure called?
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Lateral surface area is found by adding the areas of the vertical faces.
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What is the surface area formula for a cube?
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What is the surface area formula for a cylinder?
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What is the surface area formula for a rectangular prism?
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What is the surface area formula for a sphere?
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What is the surface area formula for a square pyramid?
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What is the surface area of a rectangular prism if it is 36 m²?
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What is the surface area of a cylinder if it is 314 sq.ft.?
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What is the surface area of a cube if it is 54 sq.yd.?
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What is the surface area of a triangular pyramid if it is 464 sq.in.?
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What is the surface area of a sphere if it is 5,024 cm²?
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Study Notes
Prisms and Polyhedra
- Prisms are polyhedra with two congruent and parallel faces.
- Tetrahedron is a triangular pyramid, not a torus (doughnut-shaped figure).
Properties of Polyhedra
- The faces of a polyhedron feature flat polygons, not curved surfaces.
- A net is a pattern of two-dimensional shapes that can be folded into a three-dimensional figure.
Surface Area Formulas
- Lateral surface area is derived by summing the areas of all vertical faces.
- Surface area (SA) formulas for various solids:
- Cube: ( SA = 6e^2 )
- Cylinder: ( SA = 2\pi rh + 2\pi r^2 )
- Rectangular Prism: ( SA = 2lw + 2wh + 2lh )
- Sphere: ( SA = 4\pi r^2 )
- Square Pyramid: ( SA = 4(1/2bh) + b^2 )
Surface Area Calculations
- A rectangular prism's surface area is 36 m².
- The surface area of a cylinder is 314 square feet.
- The surface area of a cube is 54 square yards.
- A triangular pyramid has a surface area of 464 square inches.
- The surface area of a sphere is 5,024 cm².
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Test your knowledge with Abeka's Pre-Algebra Quiz 20 flashcards. This quiz focuses on key concepts related to polyhedra, including definitions and properties. Perfect for students looking to reinforce their understanding in geometry and spatial reasoning.
