Question
Julissa is planning on wrapping a present in a shoe box. The shoe box has a length of 14 in
, a width of 10 in
, and a height of 5 in
.
What is the minimum amount of wrapping paper needed to cover the box?
Responses
A
280 in squared
B
560 in squared
C
700 in squared
D
, a width of 10 in
, and a height of 5 in
.
What is the minimum amount of wrapping paper needed to cover the box?
Responses
A
280 in squared
B
560 in squared
C
700 in squared
D
Answers
GPT-4o mini
To find the minimum amount of wrapping paper needed to cover the shoe box, we need to calculate the surface area of the box. The formula for the surface area \( A \) of a rectangular prism (which a shoebox is) is given by:
\[
A = 2(lw + lh + wh)
\]
where:
- \( l \) is the length
- \( w \) is the width
- \( h \) is the height
Given:
- \( l = 14 \) in
- \( w = 10 \) in
- \( h = 5 \) in
Now we will plug in the values into the formula:
1. Calculate \( lw \):
\[
lw = 14 \times 10 = 140 \, \text{in}^2
\]
2. Calculate \( lh \):
\[
lh = 14 \times 5 = 70 \, \text{in}^2
\]
3. Calculate \( wh \):
\[
wh = 10 \times 5 = 50 \, \text{in}^2
\]
4. Now, sum these areas:
\[
lw + lh + wh = 140 + 70 + 50 = 260 \, \text{in}^2
\]
5. Finally, multiply by 2 to get the total surface area:
\[
A = 2 \times 260 = 520 \, \text{in}^2
\]
Thus, the minimum amount of wrapping paper needed to cover the box is \( 520 \, \text{in}^2 \).
However, since this specific value is not listed among the responses provided, it appears there may be an error in the response options. It could also be helpful to double-check the calculations or confirm the given dimensions and responses. Based on our calculations, the correct answer is **520 in squared**.
\[
A = 2(lw + lh + wh)
\]
where:
- \( l \) is the length
- \( w \) is the width
- \( h \) is the height
Given:
- \( l = 14 \) in
- \( w = 10 \) in
- \( h = 5 \) in
Now we will plug in the values into the formula:
1. Calculate \( lw \):
\[
lw = 14 \times 10 = 140 \, \text{in}^2
\]
2. Calculate \( lh \):
\[
lh = 14 \times 5 = 70 \, \text{in}^2
\]
3. Calculate \( wh \):
\[
wh = 10 \times 5 = 50 \, \text{in}^2
\]
4. Now, sum these areas:
\[
lw + lh + wh = 140 + 70 + 50 = 260 \, \text{in}^2
\]
5. Finally, multiply by 2 to get the total surface area:
\[
A = 2 \times 260 = 520 \, \text{in}^2
\]
Thus, the minimum amount of wrapping paper needed to cover the box is \( 520 \, \text{in}^2 \).
However, since this specific value is not listed among the responses provided, it appears there may be an error in the response options. It could also be helpful to double-check the calculations or confirm the given dimensions and responses. Based on our calculations, the correct answer is **520 in squared**.