Question

An illustration shows a 3 D box with length of 36 inches labeled as front, a width of 28 inches, and height of 25 inches. A line on either side of the box runs along the length of the top and front. The space between the line and the edge of the box is labeled 3 inches on each side.
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)
Responses

5,216 in.2
5,216 in squared

318 in.2
318 in. squared

636 in.2
636 in. squared

1,400 in.2

Answer 1

To calculate the surface area of the trim that needs to be painted around the edge of the trunk, we first need to determine the overall dimensions of the area to be painted.

Given dimensions of the box are:
- Length = 36 inches
- Width = 28 inches
- Height = 25 inches

Since the trim is labeled as 3 inches on either side along the length and width, we need to add these dimensions to the box's original dimensions.

1. **Calculate the trimmed dimensions:**
- The overall length with the trim on both sides:
\( 36 + 3 + 3 = 36 + 6 = 42 \) inches
- The overall width with the trim on both sides:
\( 28 + 3 + 3 = 28 + 6 = 34 \) inches
- The height remains the same since trim is applied around the edges, which doesn't affect the height.

2. **Calculate the surface area of the outer box (with trim):**
The surface area of a rectangular box is calculated using the formula:
\[
\text{Surface Area} = 2lw + 2lh + 2wh
\]
where \( l \) is the length, \( w \) is the width, and \( h \) is the height.

Plugging in the trimmed dimensions:
- Length \( = 42 \)
- Width \( = 34 \)
- Height \( = 25 \)

Now, calculate:
\[
\text{Surface Area} = 2(42)(34) + 2(42)(25) + 2(34)(25)
\]
- Calculate each term:
- \( 2(42)(34) = 2(1428) = 2856 \)
- \( 2(42)(25) = 2(1050) = 2100 \)
- \( 2(34)(25) = 2(850) = 1700 \)

Now sum these up:
\[
\text{Total Surface Area} = 2856 + 2100 + 1700 = 6656 \text{ in}^2
\]

3. **Calculate the surface area of the inner box (without trim):**
The inner dimensions are the original box dimensions:
- Length = 36 inches
- Width = 28 inches
- Height = 25 inches

Now calculate:
\[
\text{Surface Area} = 2(36)(28) + 2(36)(25) + 2(28)(25)
\]

Calculate each term:
- \( 2(36)(28) = 2(1008) = 2016 \)
- \( 2(36)(25) = 2(900) = 1800 \)
- \( 2(28)(25) = 2(700) = 1400 \)

Now sum these up:
\[
\text{Total Surface Area} = 2016 + 1800 + 1400 = 5216 \text{ in}^2
\]

4. **Find the surface area of the trim to be painted:**
Now subtract the surface area of the inner box from the outer box:
\[
\text{Surface Area of Trim} = 6656 - 5216 = 1440 \text{ in}^2
\]

Since none of the options you provided match, I believe the intent in this exercise is to capture the trim area surface which is derived to be 1440 in². If you have specific choices from which to choose, please adjust or clarify as necessary.