So I have this L-shaped sofa with dimensions provided, and I need to find its volume. The measurements are as follows:
First, I need to understand the shape and how it affects the volume calculation. An L-shaped sofa consists of two main parts: the straight section and the chaise lounge section.
Let me visualize this:
The straight section is 300 cm in length and 90 cm in depth.
The chaise section extends from the straight section, adding another 180 cm in depth and 90 cm in width.
To find the volume, I should consider the sofa as a combination of rectangular prisms.
Perhaps I can divide the sofa into two parts:
The straight section: a rectangular prism with dimensions 300 cm x 90 cm x 90 cm.
The chaise section: another rectangular prism with dimensions 180 cm x 90 cm x 90 cm.
Wait, but when I look at the dimensions, the chaise section is 180 cm in depth and 90 cm in width. However, since it’s an L-shape, the width of the chaise section might overlap with the straight section.
Let me double-check the dimensions.
Looking at the image:
The overall length is 300 cm.
The width is 90 cm for both sections.
The depth of the chaise is 180 cm.
I think the straight section is 300 cm in length and 90 cm in width, and the chaise section is 180 cm in depth and 90 cm in width, attached to the straight section.
In this case, the volume would be the sum of the volumes of these two sections.
First, calculate the volume of the straight section:
Volume_straight = length x width x height
Here, length = 300 cm, width = 90 cm, and height = 90 cm.
Volume_straight = 300 cm x 90 cm x 90 cm
Wait, but I need to confirm if the height is indeed 90 cm. The image shows a vertical dimension of 90 cm, which could be the height.
So, Volume_straight = 300 cm x 90 cm x 90 cm
Similarly, for the chaise section:
Volume_chaise = depth x width x height
Depth = 180 cm, width = 90 cm, height = 90 cm.
Volume_chaise = 180 cm x 90 cm x 90 cm
Then, the total volume would be Volume_total = Volume_straight + Volume_chaise
Let me calculate that.
First, Volume_straight = 300 cm x 90 cm x 90 cm = 2,430,000 cubic cm
Second, Volume_chaise = 180 cm x 90 cm x 90 cm = 1,458,000 cubic cm
Total volume = 2,430,000 + 1,458,000 = 3,888,000 cubic cm
But, I should consider if there’s any overlap or shared volume between the two sections.
Looking back, in an L-shape, the chaise section shares some space with the straight section, so perhaps simply adding the volumes isn’t accurate.
Maybe I should think of the entire sofa as a single rectangular prism with length 300 cm, width 180 cm (since the chaise adds 180 cm to the width), and height 90 cm.
Wait, but the width of the straight section is 90 cm, and the chaise adds another 90 cm to the width, making the total width 180 cm.
So, total dimensions would be:
Length: 300 cm
Width: 180 cm
Height: 90 cm
Therefore, total volume = length x width x height = 300 cm x 180 cm x 90 cm = 4,860,000 cubic cm
However, this seems larger than the previous calculation. Which one is correct?
Let me think again.
Option 1: Sum of two separate volumes:
Volume_straight + Volume_chaise = 2,430,000 + 1,458,000 = 3,888,000 cubic cm
Option 2: Entire sofa as one big rectangular prism:
Volume_total = 300 cm x 180 cm x 90 cm = 4,860,000 cubic cm
But this seems incorrect because it’s overcounting the shared space where the two sections meet.
So, Option 1 is more accurate.
Alternatively, perhaps I need to consider the chaise section as an extension that doesn’t add its full volume but only the additional volume it provides.
Wait, maybe I should subtract the overlapping volume.
Let me try another approach.
Consider the straight section as a rectangular prism: 300 cm x 90 cm x 90 cm.
The chaise section extends 180 cm in depth and 90 cm in width, but since it’s attached to the straight section, there is an overlap in width.
Actually, in an L-shape, the chaise section shares the width with the straight section, so the additional volume added by the chaise is only the part that doesn’t overlap.
Wait, this is getting complicated.
Maybe I should look at it differently.
Let’s consider the entire base area first.
The base of the sofa would be the area in contact with the floor.
The straight section is 300 cm in length and 90 cm in width.
The chaise section adds another 180 cm in depth, making the total width 90 cm + 180 cm = 270 cm.
Wait, no, if the straight section is 300 cm in length and 90 cm in width, and the chaise adds 180 cm in depth, then the base area would be a rectangle of 300 cm x 180 cm.
But that doesn’t account for the L-shape properly.
Alternatively, perhaps the base is L-shaped, with one side 300 cm and the other 180 cm, intersecting at a corner.
In that case, the total base area would be:
Area_base = (300 cm x 90 cm) + (180 cm x 90 cm) - (overlap area)
But what is the overlap area?
If the chaise section is attached to the straight section, the overlap would be the area where they connect.
Assuming they connect at a 90-degree angle, the overlap would be a square of side 90 cm.
Therefore, Area_overlap = 90 cm x 90 cm = 8,100 square cm
Thus, Area_base = (300 cm x 90 cm) + (180 cm x 90 cm) - 8,100 square cm
Calculate that:
(27,000 square cm) + (16,200 square cm) = 43,200 square cm
Minus 8,100 square cm = 35,100 square cm
Then, the height is 90 cm, so Volume_total = Area_base x height = 35,100 square cm x 90 cm = 3,159,000 cubic cm
This is different from both previous calculations.
Which one is correct?
I think this method accounts for the overlap properly.
Alternatively, perhaps I can use integration to find the volume, but that might be overkill for this problem.
Wait, another way: divide the sofa into smaller rectangular prisms whose volumes can be added up accurately.
Let’s try that.
Divide the sofa into three parts:
The main seat section: 300 cm x 90 cm x 90 cm
The chaise section: 180 cm x 90 cm x 90 cm
Subtract the overlapping part: 90 cm x 90 cm x 90 cm
Then, Volume_total = (300 cm x 90 cm x 90 cm) + (180 cm x 90 cm x 90 cm) - (90 cm x 90 cm x 90 cm)
Calculate each part:
Volume_main = 300 cm x 90 cm x 90 cm = 2,430,000 cubic cm
Volume_chaise = 180 cm x 90 cm x 90 cm = 1,458,000 cubic cm
Volume_overlap = 90 cm x 90 cm x 90 cm = 729,000 cubic cm
Therefore, Volume_total = 2,430,000 + 1,458,000 - 729,000 = 3,159,000 cubic cm
This matches the previous calculation using the base area method.
So, the correct volume is 3,159,000 cubic cm.
But wait, earlier I thought the total base area was 35,100 square cm multiplied by 90 cm, which gives 3,159,000 cubic cm.
Yes, that seems consistent.
Therefore, the volume of the sofa is 3,159,000 cubic cm.
Final Answer
$$ \boxed{3159000\ \text{cubic cm}} $$
