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Mathematics

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LiRa [457]4 years ago

6 0

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Margaret is building storage boxes. each box will have a length of 8 feet, a width of 512 feet, and a height of 412 feet. a pint

Lera25 [3.4K]

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,

$\rm \text{Surface area of the box}= 2[(Length \times width)+(Width \times Height)+(Length \times height)]$

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,

$\rm \text{Surface area of the box}= 2[(Length \times width)+(Width \times Height)+(Length \times height)]$

$\rm \text{Surface area of the box}= 2[(8\times 5.5)+(5.5\times 4.5)+(8 \times 4.5)] = 209.5\ ft^2$

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,

$\text{Paint Required} = \dfrac{\text{Total area that is needed to be paint}}{\text{Area covered in a pint of paint}}$

$\rm \text{Paint Required} = \dfrac{209.5}{50} = 4.19\ pints$

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,

$\text{Paint required to paint 3 boxes} = 3 \times 4.19 = 12.57 \approx 13$