To determine the different values noted in your examples, you would use specific calculations for surface area and volume based on the shapes involved. Here's a breakdown for each scenario:
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The amount of cereal a cereal box can hold:
- Calculation Needed: Volume
- Formula: For a rectangular box, the volume \( V \) is calculated using \( V = \text{length} \times \text{width} \times \text{height} \).
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The amount of paint needed to paint the sides of a house:
- Calculation Needed: Surface Area
- Formula: If the house is modeled as a rectangular prism, the surface area \( A \) can be calculated using \( A = 2(\text{length} \times \text{width} + \text{length} \times \text{height} + \text{width} \times \text{height}) \).
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The amount of wrapping paper needed to wrap a gift:
- Calculation Needed: Surface Area
- Formula: If the gift is in the shape of a rectangular box, use the same formula as above for surface area, or for a cylinder, use \( A = 2\pi r(h + r) \) where \( r \) is the radius and \( h \) is the height.
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The amount of water a bottle can hold:
- Calculation Needed: Volume
- Formula: The volume of a cylinder can be calculated using \( V = \pi r^2 h \), where \( r \) is the radius and \( h \) is the height. If the bottle is a different shape, the formula would vary accordingly.
In summary:
- Use volume calculations for capacities (cereal box, water bottle).
- Use surface area calculations for materials needed to cover surfaces (paint, wrapping paper).