Question

Which calculation would be needed to find each of the following?

Surface area and volume

the amount od cereal a cereal box can hold
the amount of paint needed to paint the sides of a house
the house amount or wrapping paper needed to wrap a girf
the amount of water a bottle can hold

Answer 1

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:

1. **The amount of cereal a cereal box can hold**:
- **Calculation Needed**: Volume
- **Formula**: For a rectangular box, the volume \( V \) is calculated using \( V = \text{length} \times \text{width} \times \text{height} \).

2. **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 \( A = 2(\text{length} \times \text{width} + \text{length} \times \text{height} + \text{width} \times \text{height}) \).

3. **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.

4. **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).