Respuesta :
Answer:the last option
Step-by-step explanation: use the step by step equation
The composite figure having the greatest surface area is 2 rectangular prisms. One prism has a length of 2, width of 1, and height of 1. The second prism has a length of 2, width of 2, and height of 2.
The correct answer is option (A).
What is surface area?
"The surface area of a three-dimensional object is the total area of all its faces. "
What is the surface are of a rectangular prism?
A = 2 × (w × l + h × l + h × w)
where 'l' represents the length of a prism, 'w' represents the width and 'h' represents the height of the prism.
What is the surface area of a cube?
A = 6 × a^(2), where 'a' represents the side length of the cube.
We find the surface area of each figure.
1) 2 rectangular prisms.
Let [tex]A_1,A_2[/tex] represents the area of smaller and larger rectangular prisms respectively.
Dimensions of the smaller rectangular prism,
length = 2, width = 1, height = 1.
So, the surface area of the smaller rectangular prism would be,
[tex]\Rightarrow A_1=2\times (lw+lh+hw)\\\Rightarrow A_1=2\times ((2\times 2)+(2\times 1)+(1\times 2))\\\Rightarrow A_1=2\times (4+2+2)\\\Rightarrow A_1=2\times 8\\\Rightarrow A_1 =16~~square~units[/tex]
Dimensions of the second rectangular prism has a length of 2, width of 2, and height of 2.
So, the surface area of the larger rectangular prism would be,
[tex]\Rightarrow A_2=2\times (lw+lh+hw)\\\Rightarrow A_2=2\times ((2\times 2)+(2\times 2)+(2\times 2))\\\Rightarrow A_2=2\times (4+4+4)\\\Rightarrow A_2=2\times 12\\\Rightarrow A_2=24~~square~units[/tex]
Now, the total surface area of the figure would be,
[tex]=A_1+A_2\\=16+24\\=\bold{40~~square~ units}[/tex]
2) A rectangular prism
dimensions: - a length of 1, width of 1, and height of 2
The surface area for a given rectangular prism would be,
⇒ A = 2 × ((w × l) + (h × l) + (h × w))
⇒ A = 2 × ((1 × 1) + (2 × 1) + (2 × 1))
⇒ A = 2 × (1 + 2 + 2)
⇒ A = 2 × (5)
⇒ A = 10 square units
3) 2 rectangular prisms
Let [tex]A_1,A_2[/tex] represents the area of the first and the second rectangular prisms respectively.
Dimensions of the first rectangular prism,
length = 2, width = 2, height = 1.
So, the surface area of the first rectangular prism would be,
[tex]\Rightarrow A_1=2\times (lw+lh+hw)\\\Rightarrow A_1=2\times ((2\times 2)+(2\times 1)+(1\times 2))\\\Rightarrow A_1=2\times (4+2+2)\\\Rightarrow A_1=2\times 8\\\Rightarrow A_1 =16~~square~units[/tex]
Dimensions of the second rectangular prism has a length of 2, width of 1, and height of 1.
So, the surface area of the second rectangular prism would be,
[tex]\Rightarrow A_2=2\times (lw+lh+hw)\\\Rightarrow A_2=2\times ((2\times 1)+(2\times 1)+(1\times 1))\\\Rightarrow A_2=2\times (2+2+1)\\\Rightarrow A_2=2\times 5\\\Rightarrow A_2 =10~~square~units[/tex]
Now, the total surface area of the figure would be,
[tex]=A_1+A_2\\=16+10\\=\bold{26~~square~ units}[/tex]
4) a cube
dimension: side length (a) = 2
The surface area of a cube would be,
[tex]\Rightarrow A=6\times a^{2} \\\Rightarrow A=6\times 2^{2} \\\Rightarrow A=6\times 4\\\Rightarrow A=\bold{24~~square~units}[/tex]
Therefore, the composite figure having the greatest surface area is 2 rectangular prisms. One prism has a length of 2, width of 1, and height of 1. The second prism has a length of 2, width of 2, and height of 2.
The correct answer is option (A).
Learn more about surface area here:
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