Question
Surface Area of Right Rectangular Prisms Quick Check
4 of 54 of 5 Items
Question
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 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 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 A will require less wrapping paper because its surface area is 1.5 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.
Book B will require less wrapping paper because its surface area is 0.5 in.2
less than the surface area of Book A.
4 of 54 of 5 Items
Question
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 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 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 A will require less wrapping paper because its surface area is 1.5 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.
Book B will require less wrapping paper because its surface area is 0.5 in.2
less than the surface area of Book A.
Answers
GPT-4o mini
To determine which book requires less wrapping paper, we need to calculate the surface areas of Book A and Book B.
The formula for the surface area \(S\) of a right rectangular prism is:
\[
S = 2(lw + lh + wh)
\]
where \(l\) is the length, \(w\) is the width, and \(h\) is the height.
**For Book A:**
- Length \(l = 6.5\) inches
- Width \(w = 1\) inch
- Height \(h = 8.5\) inches
Calculating the surface area:
\[
S_A = 2((6.5 \times 1) + (6.5 \times 8.5) + (1 \times 8.5))
\]
\[
= 2(6.5 + 55.25 + 8.5)
\]
\[
= 2(70.25)
\]
\[
= 140.5 \, \text{in}^2
\]
**For Book B:**
- Length \(l = 5.5\) inches
- Width \(w = 2\) inches
- Height \(h = 8\) inches
Calculating the surface area:
\[
S_B = 2((5.5 \times 2) + (5.5 \times 8) + (2 \times 8))
\]
\[
= 2(11 + 44 + 16)
\]
\[
= 2(71)
\]
\[
= 142 \, \text{in}^2
\]
Now we compare the surface areas:
- Surface area of Book A: \(140.5 \, \text{in}^2\)
- Surface area of Book B: \(142 \, \text{in}^2\)
Since \(140.5 < 142\), Book A has a smaller surface area.
**Conclusion:**
Book A will require less wrapping paper because its surface area is \(1.5 \, \text{in}^2\) less than the surface area of Book B.
The correct response is:
**Book A will require less wrapping paper because its surface area is 1.5 in.² less than the surface area of Book B.**
The formula for the surface area \(S\) of a right rectangular prism is:
\[
S = 2(lw + lh + wh)
\]
where \(l\) is the length, \(w\) is the width, and \(h\) is the height.
**For Book A:**
- Length \(l = 6.5\) inches
- Width \(w = 1\) inch
- Height \(h = 8.5\) inches
Calculating the surface area:
\[
S_A = 2((6.5 \times 1) + (6.5 \times 8.5) + (1 \times 8.5))
\]
\[
= 2(6.5 + 55.25 + 8.5)
\]
\[
= 2(70.25)
\]
\[
= 140.5 \, \text{in}^2
\]
**For Book B:**
- Length \(l = 5.5\) inches
- Width \(w = 2\) inches
- Height \(h = 8\) inches
Calculating the surface area:
\[
S_B = 2((5.5 \times 2) + (5.5 \times 8) + (2 \times 8))
\]
\[
= 2(11 + 44 + 16)
\]
\[
= 2(71)
\]
\[
= 142 \, \text{in}^2
\]
Now we compare the surface areas:
- Surface area of Book A: \(140.5 \, \text{in}^2\)
- Surface area of Book B: \(142 \, \text{in}^2\)
Since \(140.5 < 142\), Book A has a smaller surface area.
**Conclusion:**
Book A will require less wrapping paper because its surface area is \(1.5 \, \text{in}^2\) less than the surface area of Book B.
The correct response is:
**Book A will require less wrapping paper because its surface area is 1.5 in.² less than the surface area of Book B.**