A wooden box is 1 foot high, 3 feet wide, and 5 feet long. Bob is going to use it for a table top and plans to paint the 4 sides and top. How many square feet will be painted?A. 15 B. 30 C. 31 D. 46

Calculate the area of the 4 sides and the top of the box.

1. \[Area\text { } of \text { } the \text { } top ( length \times width) : \]
   \[5 \text { ft} \times 3 \text { ft} = 15 \text { sq ft} \]
2. \[Area \text { } of\text { } the \text { } two \text { } longer\text { } sides ( length \times height, and there are 2 of these sides) : \]
   \[2 \times ( 5 \text { ft} \times 1 \text { ft} ) = 2 \times 5 \text { sq ft} = 10 \text { sq ft} \]
3. \[Area\text { } of \text { } the\text { } two \text { } shorter \text { } sides ( width \times height, and\text { } there \text { } are \text { } 2 \text { } of \text { } these\text { } sides) : \]
   \[2 \times ( 3 \text { ft} \times 1 \text { ft} ) = 2 \times 3 \text { sq ft} = 6 \text { sq ft} \]
4. Total area to be painted:
   \[15 \text { sq ft} + 10 \text { sq ft} + 6 \text { sq ft} = 31 \text { sq ft} \]
   So, the total area that will be painted is 31 square feet.

Supplemental Knowledge

Calculating the surface area of three-dimensional objects requires adding together all their areas; when used to describe rectangular prisms (such as wooden boxes), their surface areas are determined by separately calculating each face and then adding them together.
A rectangular prism has six faces:

Two pairs of opposite faces with identical dimensions (length × width, width × height, and height × length).
When calculating the surface area for painting purposes, you only need to consider the specific faces that will be painted.

Concepts to Actions

Understanding how to calculate surface area is essential in various practical scenarios:

• Home Improvement: When painting walls or furniture, knowing the surface area helps estimate how much paint you’ll need.
• Packaging Design: Companies use surface area calculations to determine material requirements for boxes and containers.

Imagine Bob wants to turn an old wooden box into a table. By carefully calculating how much paint will cover his table's surface area, he can ensure he purchases only enough paint for perfect coverage - saving both time and money while producing an ideal finish finish.

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