To find the required measurements for each of the items you've mentioned, you would typically utilize specific formulas based on their geometrical shapes. Here's a breakdown for each:
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Surface Area:
- The formula required depends on the shape. For a rectangular prism (like a box), the surface area (SA) can be calculated as: \[ SA = 2(lw + lh + wh) \] where \(l\) is length, \(w\) is width, and \(h\) is height. For other shapes, there are different formulas.
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Volume:
- For a rectangular prism (like a box), the volume (V) can be found using: \[ V = l \times w \times h \]
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The amount of cereal a cereal box can hold (which is essentially its volume):
- Use the same volume formula as above for a rectangular prism (if the cereal box is rectangular). \[ V = l \times w \times h \]
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The amount of paint needed to paint the sides of a house (assuming the house is a rectangular prism):
- You would calculate the surface area of the structure (similar to point 1): \[ SA = 2(lw + lh + wh) \]
- Then, based on the surface area, determine how much paint is required (considering the coverage rate of the paint).
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The amount of wrapping paper needed to wrap a gift:
- This also depends on the shape of the gift (often a rectangular prism). You can use the surface area formula: \[ SA = 2(lw + lh + wh) \]
- If the gift is a different shape (like a cylinder), then the appropriate surface area formula for that shape should be used.
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The amount of water a bottle can hold (assuming the bottle is cylindrical):
- Use the volume formula for a cylinder: \[ V = \pi r^2 h \]
- where \(r\) is the radius of the base and \(h\) is the height of the bottle.
In summary:
- For surface area, use surface area formulas.
- For volume, use volume formulas specific to the shapes involved.