The surface area of a cuboid is the area of all the six faces of a cuboid. The Paint that is required to paint 3 boxes is 13 pints.
<h3>What is the surface area of a cuboid?</h3>
The surface area of a cuboid is the area of all the six faces of a cuboid. It is given by the formula,
![\rm \text{Surface area of the box}= 2[(Length \times width)+(Width \times Height)+(Length \times height)]](https://tex.z-dn.net/?f=%5Crm%20%5Ctext%7BSurface%20area%20of%20the%20box%7D%3D%202%5B%28Length%20%5Ctimes%20width%29%2B%28Width%20%5Ctimes%20Height%29%2B%28Length%20%5Ctimes%20height%29%5D)
As it is given the dimensions of the storage box are a length of 8 feet, a width of 5 1/2 feet(5.5 feet), and a height of 4 1/2 feet(4.5 feet). Therefore, the surface area of the box can be written as,
![\rm \text{Surface area of the box}= 2[(Length \times width)+(Width \times Height)+(Length \times height)]](https://tex.z-dn.net/?f=%5Crm%20%5Ctext%7BSurface%20area%20of%20the%20box%7D%3D%202%5B%28Length%20%5Ctimes%20width%29%2B%28Width%20%5Ctimes%20Height%29%2B%28Length%20%5Ctimes%20height%29%5D)
![\rm \text{Surface area of the box}= 2[(8\times 5.5)+(5.5\times 4.5)+(8 \times 4.5)] = 209.5\ ft^2](https://tex.z-dn.net/?f=%5Crm%20%5Ctext%7BSurface%20area%20of%20the%20box%7D%3D%202%5B%288%5Ctimes%205.5%29%2B%285.5%5Ctimes%204.5%29%2B%288%20%5Ctimes%204.5%29%5D%20%3D%20209.5%5C%20ft%5E2)
As it is given that the surface area that can be covered with a pint of paint is 50 square feet, therefore, the paint that will be required to paint 209 square feet is,
![\text{Paint Required} = \dfrac{\text{Total area that is needed to be paint}}{\text{Area covered in a pint of paint}}](https://tex.z-dn.net/?f=%5Ctext%7BPaint%20Required%7D%20%3D%20%5Cdfrac%7B%5Ctext%7BTotal%20area%20that%20is%20needed%20to%20be%20paint%7D%7D%7B%5Ctext%7BArea%20covered%20in%20a%20pint%20of%20paint%7D%7D)
![\rm \text{Paint Required} = \dfrac{209.5}{50} = 4.19\ pints](https://tex.z-dn.net/?f=%5Crm%20%5Ctext%7BPaint%20Required%7D%20%3D%20%5Cdfrac%7B209.5%7D%7B50%7D%20%3D%204.19%5C%20pints)
Now, we know that the surface area of the box is 209 square feet, while the paint required to paint a complete box is 4.19, therefore, the paint that will be required to paint 3 boxes will be,
![\text{Paint required to paint 3 boxes} = 3 \times 4.19 = 12.57 \approx 13](https://tex.z-dn.net/?f=%5Ctext%7BPaint%20required%20to%20paint%203%20boxes%7D%20%3D%203%20%5Ctimes%204.19%20%3D%2012.57%20%5Capprox%2013)
Hence, the Paint that is required to paint 3 boxes is 13 pints.
Learn more about Surface Area of Cuboid:
brainly.com/question/26403859