Question
Find the surface area of a textbook that is 2 in. × 14 in. × 9 in. (1 point)
• 344 in.?
• 50 in.?
• 172 in.?
O 252 in.?
• 344 in.?
• 50 in.?
• 172 in.?
O 252 in.?
Answers
Answer
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)
A. Book B will require less wrapping paper because its surface area is 0.5 in." less than the surface area of Book A.
B. Book A will require less wrapping paper because its surface area is 32.75 in.? less than the surface area of Book B.
C. Book B will require less wrapping paper because its surface area is 1.5 in.? less than the surface area of Book A.
D. Book A will require less wrapping paper because its surface area is 1.5 in." less than the surface area of Book B.
A. Book B will require less wrapping paper because its surface area is 0.5 in." less than the surface area of Book A.
B. Book A will require less wrapping paper because its surface area is 32.75 in.? less than the surface area of Book B.
C. Book B will require less wrapping paper because its surface area is 1.5 in.? less than the surface area of Book A.
D. Book A will require less wrapping paper because its surface area is 1.5 in." less than the surface area of Book B.
Answer
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 114 in.? and 304 in.?. How would you distinguish which answer is lateral surface area and which is total surface area? (1 point)
The lateral surface area is 144 in.?, and the total surface area is 304 in.?. The area that is less is the lateral surface area.
The lateral surface area is 304 in." and the total surface area is 144 in.?. The greater area is the lateral surface area.
• The two areas should be the same, so Jenny should recalculate.
• There is not enough information given to distinguish lateral surface area from total surface area.
The lateral surface area is 144 in.?, and the total surface area is 304 in.?. The area that is less is the lateral surface area.
The lateral surface area is 304 in." and the total surface area is 144 in.?. The greater area is the lateral surface area.
• The two areas should be the same, so Jenny should recalculate.
• There is not enough information given to distinguish lateral surface area from total surface area.
Answered by
GPT 3.5
To find the surface area of a textbook, you need to calculate the area of each individual side and then add them together.
The textbook has six sides:
- Two sides with dimensions 2 in. × 14 in., so each side has an area of (2 in.)(14 in.) = 28 in².
- Two sides with dimensions 14 in. × 9 in., so each side has an area of (14 in.)(9 in.) = 126 in².
- Two sides with dimensions 2 in. × 9 in., so each side has an area of (2 in.)(9 in.) = 18 in².
Adding up the areas of all the sides, we get:
(28 in²) + (28 in²) + (126 in²) + (126 in²) + (18 in²) + (18 in²) = 344 in²
Therefore, the correct answer is 344 in².
The textbook has six sides:
- Two sides with dimensions 2 in. × 14 in., so each side has an area of (2 in.)(14 in.) = 28 in².
- Two sides with dimensions 14 in. × 9 in., so each side has an area of (14 in.)(9 in.) = 126 in².
- Two sides with dimensions 2 in. × 9 in., so each side has an area of (2 in.)(9 in.) = 18 in².
Adding up the areas of all the sides, we get:
(28 in²) + (28 in²) + (126 in²) + (126 in²) + (18 in²) + (18 in²) = 344 in²
Therefore, the correct answer is 344 in².
Answered by
GPT 3.5
To find the surface area of each book, you need to calculate the area of each individual side and then add them together.
For Book A:
- The sides with dimensions 6.5 in. × 1 in. have an area of (6.5 in.)(1 in.) = 6.5 in².
- The sides with dimensions 6.5 in. × 8.5 in. have an area of (6.5 in.)(8.5 in.) = 55.25 in².
- The sides with dimensions 8.5 in. × 1 in. have an area of (8.5 in.)(1 in.) = 8.5 in².
The surface area of Book A is:
(6.5 in²) + (6.5 in²) + (55.25 in²) + (55.25 in²) + (8.5 in²) + (8.5 in²) = 140.5 in².
For Book B:
- The sides with dimensions 5.5 in. × 2 in. have an area of (5.5 in.)(2 in.) = 11 in².
- The sides with dimensions 5.5 in. × 8 in. have an area of (5.5 in.)(8 in.) = 44 in².
- The sides with dimensions 8 in. × 2 in. have an area of (8 in.)(2 in.) = 16 in².
The surface area of Book B is:
(11 in²) + (11 in²) + (44 in²) + (44 in²) + (16 in²) + (16 in²) = 142 in².
Comparing the surface areas of both books, we can see that Book A has a surface area of 140.5 in², while Book B has a surface area of 142 in².
Therefore, the correct answer is: Book A will require less wrapping paper because its surface area is 1.5 in² less than the surface area of Book B. Option D.
For Book A:
- The sides with dimensions 6.5 in. × 1 in. have an area of (6.5 in.)(1 in.) = 6.5 in².
- The sides with dimensions 6.5 in. × 8.5 in. have an area of (6.5 in.)(8.5 in.) = 55.25 in².
- The sides with dimensions 8.5 in. × 1 in. have an area of (8.5 in.)(1 in.) = 8.5 in².
The surface area of Book A is:
(6.5 in²) + (6.5 in²) + (55.25 in²) + (55.25 in²) + (8.5 in²) + (8.5 in²) = 140.5 in².
For Book B:
- The sides with dimensions 5.5 in. × 2 in. have an area of (5.5 in.)(2 in.) = 11 in².
- The sides with dimensions 5.5 in. × 8 in. have an area of (5.5 in.)(8 in.) = 44 in².
- The sides with dimensions 8 in. × 2 in. have an area of (8 in.)(2 in.) = 16 in².
The surface area of Book B is:
(11 in²) + (11 in²) + (44 in²) + (44 in²) + (16 in²) + (16 in²) = 142 in².
Comparing the surface areas of both books, we can see that Book A has a surface area of 140.5 in², while Book B has a surface area of 142 in².
Therefore, the correct answer is: Book A will require less wrapping paper because its surface area is 1.5 in² less than the surface area of Book B. Option D.
Answered by
GPT 3.5
To determine which answer is the lateral surface area and which is the total surface area, we need to understand the definitions of these two terms.
The lateral surface area refers to the sum of the areas of all the lateral faces of the prism, excluding the bases. It can also be thought of as the surface area of the "sides" of the prism.
The total surface area, on the other hand, includes not only the lateral surface but also the areas of the two bases. It represents the complete surface area of the prism.
In this case, we have an answer of 114 in² and 304 in².
Since the lateral surface area only considers the sides and does not include the bases, it is usually smaller than the total surface area.
Therefore, the answer that is smaller, 114 in², is most likely the lateral surface area. And the answer that is larger, 304 in², is most likely the total surface area.
Thus, the correct conclusion is: The lateral surface area is 114 in², and the total surface area is 304 in². The area that is less is the lateral surface area. Option A.
The lateral surface area refers to the sum of the areas of all the lateral faces of the prism, excluding the bases. It can also be thought of as the surface area of the "sides" of the prism.
The total surface area, on the other hand, includes not only the lateral surface but also the areas of the two bases. It represents the complete surface area of the prism.
In this case, we have an answer of 114 in² and 304 in².
Since the lateral surface area only considers the sides and does not include the bases, it is usually smaller than the total surface area.
Therefore, the answer that is smaller, 114 in², is most likely the lateral surface area. And the answer that is larger, 304 in², is most likely the total surface area.
Thus, the correct conclusion is: The lateral surface area is 114 in², and the total surface area is 304 in². The area that is less is the lateral surface area. Option A.
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