Use the formula for the surface area of a right rectangular prism to find the surface area of a shape with the following measurements: length = 4.5 cm, width = 3.5 cm, and height = 2.5 cm.(1 point)
Responses
10.5 cm2
10.5 cm squared
63 cm2
63 cm squared
35.75 cm2
35.75 cm squared
71.5 cm2
To find the surface area of a right rectangular prism, you need to calculate the area of each of its six faces and add them together.
The formula for the surface area of a right rectangular prism is:
Surface Area = 2lw + 2lh + 2wh
Given measurements:
Length = 4.5 cm
Width = 3.5 cm
Height = 2.5 cm
Plugging these values into the formula:
Surface Area = 2(4.5)(3.5) + 2(4.5)(2.5) + 2(3.5)(2.5)
Surface Area = 31.5 + 22.5 + 17.5
Surface Area = 71.5 cm2
Therefore, the surface area of the given shape is 71.5 cm2.
Use the formula to determine the surface area of a right rectangular prism where each edge length measures 12.75 cm.(1 point)
Responses
975.38 cm2
975.38 cm squared
459 cm2
459 cm squared
5,852.25 cm2
5,852.25 cm squared
76.5 cm2
To find the surface area of a right rectangular prism with equal edge lengths, you can use the formula:
Surface Area = 6s^2
Given measurement:
Edge Length = 12.75 cm
Plugging this value into the formula:
Surface Area = 6(12.75)^2
Surface Area = 6(162.5625)
Surface Area = 975.375 cm2
Therefore, the surface area of the given shape is 975.375 cm2.
Find the surface area of a textbook that is 2 in. × 14 in. × 9 in. (1 point)
Responses
172 in.2
172 in. squared
344 in.2
344 in. squared
252 in.2
252 in. squared
50 in.2
To find the surface area of a rectangular prism (in this case, a textbook), you need to calculate the area of each of its six faces and add them together.
Given measurements:
Length = 2 in
Width = 14 in
Height = 9 in
Let's calculate the area of each face:
- Top and bottom face: Length × Width = 2 in × 14 in = 28 in2 (each face)
- Side faces: Length × Height = 2 in × 9 in = 18 in2 (two faces)
- Front and back faces: Width × Height = 14 in × 9 in = 126 in2 (each face)
Now, sum up the areas of all the faces:
28 in2 + 28 in2 + 18 in2 + 18 in2 + 126 in2 + 126 in2 = 344 in2
Therefore, the surface area of the textbook is 344 in2.
Sue is wrapping books to give as gifts. Book A has a length of 6.5 inches, a width of 1 inch, and a height of 8.5 inches. Book B has a length of 5.5 inches, a width of 2 inches, and a height of 8 inches. Based on surface area, which book will require less wrapping paper?(1 point)
Responses
Book B will require less wrapping paper because its surface area is 1.5 in.2
less than the surface area of Book A.
Book B will require less wrapping paper because its surface area is 1.5 in.2
less than the surface area of Book A.
Book B will require less wrapping paper because its surface area is 0.5 in.2
less than the surface area of Book A.
Book B will require less wrapping paper because its surface area is 0.5 in.2
less than the surface area of Book A.
Book A will require less wrapping paper because its surface area is 32.75 in.2
less than the surface area of Book B.
Book A will require less wrapping paper because its surface area is 32.75 in.2
less than the surface area of Book B.
Book A will require less wrapping paper because its surface area is 1.5 in.2
less than the surface area of Book B.
To find the surface area of a rectangular prism (in this case, the books), you need to calculate the area of each of its six faces and compare them.
Let's calculate the surface area of each book:
Book A:
- Top and bottom face: Length × Width = 6.5 in × 1 in = 6.5 in² each
- Side faces: Length × Height = 6.5 in × 8.5 in = 55.25 in² (two faces)
- Front and back faces: Width × Height = 1 in × 8.5 in = 8.5 in² each
Total surface area of Book A: 6.5 in² + 6.5 in² + 55.25 in² + 55.25 in² + 8.5 in² + 8.5 in² = 140.5 in²
Book B:
- Top and bottom face: Length × Width = 5.5 in × 2 in = 11 in² each
- Side faces: Length × Height = 5.5 in × 8 in = 44 in² (two faces)
- Front and back faces: Width × Height = 2 in × 8 in = 16 in² each
Total surface area of Book B: 11 in² + 11 in² + 44 in² + 44 in² + 16 in² + 16 in² = 142 in²
Comparing the surface areas, we can see that Book A has a surface area of 140.5 in² and Book B has a surface area of 142 in². Therefore, Book A will require less wrapping paper since its surface area is 1.5 in² less than the surface area of Book B.
Jenny has found the total surface area and the lateral surface area of a prism, but she can’t remember which is which. She got answers of 144 in.2 and 304 in.2 . How would you distinguish which answer is lateral surface area and which is total surface area?(1 point)
Responses
The lateral surface area is 304 in.2 and the total surface area is 144 in.2. The greater area is the lateral surface area.
The lateral surface area is 304 in. squared and the total surface area is 144 in. squared . The greater area is the lateral surface area.
There is not enough information given to distinguish lateral surface area from total surface area.
There is not enough information given to distinguish lateral surface area from total surface area.
The two areas should be the same, so Jenny should recalculate.
The two areas should be the same, so Jenny should recalculate.
The lateral surface area is 144 in.2, and the total surface area is 304 in.2. The area that is less is the lateral surface area.
To distinguish between the total surface area and the lateral surface area, we need to compare the given values of 144 in.² and 304 in.².
The lateral surface area represents the area of the sides of the prism, excluding the top and bottom faces. It is usually smaller than the total surface area.
In this case, the given value of 144 in.² is smaller than 304 in.². Therefore, we can conclude that 144 in.² is the lateral surface area, and 304 in.² is the total surface area.
So, the answer is: The lateral surface area is 144 in.², and the total surface area is 304 in.². The area that is less is the lateral surface area.
Which sentence describes what it means for ideas to have cohesion?(1 point)
Responses
They are supported by evidence.
They are supported by evidence.
They are related and stick together.
They are related and stick together.
They are from sources that are up to date.
They are from sources that are up to date.
They make sense logically.