Question
The trim (shaded area) around the edge of a trunk needs to be painted. If the trim is painted all the
way around, what is the surface area to be painted?
(1 point)
5, 216 in.^2
318 in.^2
636 in.^2
1, 400 in.^2
(the front of the box is 36 inches and 28 inches wide and 25 inches tall)
way around, what is the surface area to be painted?
(1 point)
5, 216 in.^2
318 in.^2
636 in.^2
1, 400 in.^2
(the front of the box is 36 inches and 28 inches wide and 25 inches tall)
Answers
GPT-4o mini
To calculate the surface area of the trim around the edge of the trunk, we need to determine which surfaces of the trunk are involved. The given dimensions imply that the box (trunk) has:
- Height (H) = 25 in
- Width (W) = 28 in
- Length (L) = 36 in
The visible surfaces that make up the trim area are the top, front, back, and two sides.
1. **Top Surface Area** = Length × Width = 36 in × 28 in
\[
= 1,008 \, \text{in}^2
\]
2. **Front Surface Area** = Width × Height = 28 in × 25 in
\[
= 700 \, \text{in}^2
\]
3. **Back Surface Area** = Width × Height = 28 in × 25 in (same as front)
\[
= 700 \, \text{in}^2
\]
4. **Left Side Surface Area** = Height × Length = 25 in × 36 in
\[
= 900 \, \text{in}^2
\]
5. **Right Side Surface Area** = Height × Length = 25 in × 36 in (same as left)
\[
= 900 \, \text{in}^2
\]
Now, add up the areas of all the surfaces to find the total surface area that needs to be painted:
\[
\text{Total Surface Area} = \text{Top} + \text{Front} + \text{Back} + \text{Left Side} + \text{Right Side}
\]
\[
\text{Total Surface Area} = 1,008 \, \text{in}^2 + 700 \, \text{in}^2 + 700 \, \text{in}^2 + 900 \, \text{in}^2 + 900 \, \text{in}^2
\]
\[
= 1,008 + 700 + 700 + 900 + 900 = 4,208 \, \text{in}^2
\]
If we are looking for the specific area of the trim, it appears there's some misunderstanding in interpretation.
However, if we limit it just to the edge area or possibly think only about the frame around just the top of the box (counting only the perimeter around the top edges, for example), and then this calculations might differ depending on the specified area of concern.
None of the presented numbers in your options match our result of 4,208 in² directly, unless interpreting differently the edges or there are specifications of painting only the perimeter around certain areas. Please clarify whether the trim is just along certain edges or full surfaces.
- Height (H) = 25 in
- Width (W) = 28 in
- Length (L) = 36 in
The visible surfaces that make up the trim area are the top, front, back, and two sides.
1. **Top Surface Area** = Length × Width = 36 in × 28 in
\[
= 1,008 \, \text{in}^2
\]
2. **Front Surface Area** = Width × Height = 28 in × 25 in
\[
= 700 \, \text{in}^2
\]
3. **Back Surface Area** = Width × Height = 28 in × 25 in (same as front)
\[
= 700 \, \text{in}^2
\]
4. **Left Side Surface Area** = Height × Length = 25 in × 36 in
\[
= 900 \, \text{in}^2
\]
5. **Right Side Surface Area** = Height × Length = 25 in × 36 in (same as left)
\[
= 900 \, \text{in}^2
\]
Now, add up the areas of all the surfaces to find the total surface area that needs to be painted:
\[
\text{Total Surface Area} = \text{Top} + \text{Front} + \text{Back} + \text{Left Side} + \text{Right Side}
\]
\[
\text{Total Surface Area} = 1,008 \, \text{in}^2 + 700 \, \text{in}^2 + 700 \, \text{in}^2 + 900 \, \text{in}^2 + 900 \, \text{in}^2
\]
\[
= 1,008 + 700 + 700 + 900 + 900 = 4,208 \, \text{in}^2
\]
If we are looking for the specific area of the trim, it appears there's some misunderstanding in interpretation.
However, if we limit it just to the edge area or possibly think only about the frame around just the top of the box (counting only the perimeter around the top edges, for example), and then this calculations might differ depending on the specified area of concern.
None of the presented numbers in your options match our result of 4,208 in² directly, unless interpreting differently the edges or there are specifications of painting only the perimeter around certain areas. Please clarify whether the trim is just along certain edges or full surfaces.