IDNLearn.com: Your one-stop destination for finding reliable answers. Our experts provide prompt and accurate answers to help you make informed decisions on any topic.
Sagot :
To determine the amount of material needed to build the storage bin, we should calculate the surface area of the rectangular prism (also known as a rectangular box).
A rectangular prism has six faces:
- There are two identical faces for each pair of dimensions: length × width, width × height, and length × height.
1. Calculate the area of the two faces with dimensions length and width:
[tex]\[ \text{Area}_{\text{length × width}} = 2 \times (3.5 \, \text{ft} \times 2 \, \text{ft}) = 2 \times 7 \, \text{ft}^2 = 14 \, \text{ft}^2 \][/tex]
2. Calculate the area of the two faces with dimensions width and height:
[tex]\[ \text{Area}_{\text{width × height}} = 2 \times (2 \, \text{ft} \times 2.5 \, \text{ft}) = 2 \times 5 \, \text{ft}^2 = 10 \, \text{ft}^2 \][/tex]
3. Calculate the area of the two faces with dimensions length and height:
[tex]\[ \text{Area}_{\text{length × height}} = 2 \times (3.5 \, \text{ft} \times 2.5 \, \text{ft}) = 2 \times 8.75 \, \text{ft}^2 = 17.5 \, \text{ft}^2 \][/tex]
4. Sum all these areas to get the total material needed:
[tex]\[ \text{Total material needed} = 14 \, \text{ft}^2 + 10 \, \text{ft}^2 + 17.5 \, \text{ft}^2 = 41.5 \, \text{ft}^2 \][/tex]
Therefore, the amount of material needed to make the box is:
[tex]\[ \boxed{41.5 \, \text{ft}^2} \][/tex]
So, the correct answer is:
A. [tex]$41.5 ft^2$[/tex]
A rectangular prism has six faces:
- There are two identical faces for each pair of dimensions: length × width, width × height, and length × height.
1. Calculate the area of the two faces with dimensions length and width:
[tex]\[ \text{Area}_{\text{length × width}} = 2 \times (3.5 \, \text{ft} \times 2 \, \text{ft}) = 2 \times 7 \, \text{ft}^2 = 14 \, \text{ft}^2 \][/tex]
2. Calculate the area of the two faces with dimensions width and height:
[tex]\[ \text{Area}_{\text{width × height}} = 2 \times (2 \, \text{ft} \times 2.5 \, \text{ft}) = 2 \times 5 \, \text{ft}^2 = 10 \, \text{ft}^2 \][/tex]
3. Calculate the area of the two faces with dimensions length and height:
[tex]\[ \text{Area}_{\text{length × height}} = 2 \times (3.5 \, \text{ft} \times 2.5 \, \text{ft}) = 2 \times 8.75 \, \text{ft}^2 = 17.5 \, \text{ft}^2 \][/tex]
4. Sum all these areas to get the total material needed:
[tex]\[ \text{Total material needed} = 14 \, \text{ft}^2 + 10 \, \text{ft}^2 + 17.5 \, \text{ft}^2 = 41.5 \, \text{ft}^2 \][/tex]
Therefore, the amount of material needed to make the box is:
[tex]\[ \boxed{41.5 \, \text{ft}^2} \][/tex]
So, the correct answer is:
A. [tex]$41.5 ft^2$[/tex]
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. For dependable answers, trust IDNLearn.com. Thank you for visiting, and we look forward to assisting you again.