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Questions and Answers
What is the base of a solid?
What is the base of a solid?
- The total area of all the faces
- Any face that is not a base
- A plane figure that is one side of a solid figure
- A special face of a solid figure (correct)
What is a face in the context of a solid figure?
What is a face in the context of a solid figure?
A plane figure that is one side of a solid figure.
What is a lateral face?
What is a lateral face?
Any face that is not a base.
What is the definition of surface area?
What is the definition of surface area?
You multiply the length times the width times the height to find the surface area of a rectangular prism.
You multiply the length times the width times the height to find the surface area of a rectangular prism.
The surface area is the amount a solid can hold.
The surface area is the amount a solid can hold.
Surface area is measured in units cubed.
Surface area is measured in units cubed.
A rectangular prism with a length of 5 centimeters, width of 5 centimeters, and height of 10 centimeters has a surface area of 250 square centimeters.
A rectangular prism with a length of 5 centimeters, width of 5 centimeters, and height of 10 centimeters has a surface area of 250 square centimeters.
What is the surface area needed to wrap a gift measuring 8 inches by 6 inches by 10 inches?
What is the surface area needed to wrap a gift measuring 8 inches by 6 inches by 10 inches?
What is the length of each edge of a cube if its surface area is 486 square units?
What is the length of each edge of a cube if its surface area is 486 square units?
If the surface area of a rectangular prism is 442 square feet, the length is 11 feet, and the height is 8 feet, what is the width of the prism?
If the surface area of a rectangular prism is 442 square feet, the length is 11 feet, and the height is 8 feet, what is the width of the prism?
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Study Notes
Key Definitions
- Base of a Solid: The special face of a solid figure that serves as the bottom or primary surface.
- Face: A plane surface that forms one side of a solid figure.
- Lateral Face: Any face of a solid figure that is not the base.
- Surface Area: The total area of all the faces of a solid figure, represented in square units.
Surface Area Calculations
- To find the surface area of a rectangular prism, multiply the lengths of its six rectangular faces, not simply the length, width, and height.
- Common misconceptions include thinking the surface area calculation involves multiplying length, width, and height or that surface area measures the volume of the solid.
Surface Area Examples
- A rectangular prism measuring 5 cm in length, 5 cm in width, and 10 cm in height has a surface area of 250 square centimeters.
- For a gift measuring 8 inches by 6 inches by 10 inches, the surface area required for wrapping is 376 square inches.
- Determining edge length: A cube with a surface area of 486 square units has edges measuring 9 units.
- In a rectangular prism with a surface area of 442 square feet, a length of 11 feet, and a height of 8 feet, the width is calculated to be 7 feet.
Important Clarifications
- Surface area is not the amount a solid can hold; instead, it reflects the total area of all external surfaces.
- Surface area is measured in square units, not cubic units.
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