The capacity or volume of an object is 801.5cm³. Find the area of material needed to make the container in cm²
To find the area of material needed to make the container, we first need to determine the dimensions of the container. Since the capacity or volume of the object is given as 801.5cm³, we know that the volume of a rectangular prism (container) is given by the formula V = lwh, where l is the length, w is the width, and h is the height.
Given that v = 801.5cm³, we need to determine the dimensions of the box in order to calculate the area needed to make it.
One possible way is to try different combinations of length, width, and height until we find the one that works:
Let's start by trying some reasonable dimensions:
If we assume the length (l) to be 10cm, the width (w) to be 15cm, and the height (h) to be 5.34cm, the volume of the box will be:
V = lwh
V = 10 * 15 * 5.34 = 801 cm³
The dimensions of the box will be:
Length = 10 cm
Width = 15 cm
Height = 5.34 cm
Now, to find the area of material needed to make the container, we calculate the surface area of the five faces of the box:
1. Front and back faces:
Area = 2lw
Area = 2 * 10 * 5.34 = 106.8 cm²
2. Top and bottom faces:
Area = 2wh
Area = 2 * 15 * 5.34 = 160.2 cm²
3. Side faces:
Area = 2lh
Area = 2 * 10 * 5.34 = 106.8 cm²
Therefore, the total area of material needed to make the container is:
Total Area = 2lw + 2wh + 2lh
Total Area = 106.8 + 160.2 + 106.8
Total Area ≈ 373.8 cm²
Therefore, the area of material needed to make the container will be approximately 373.8 cm².
The answer is 529cm². The height of the object is 12cm and the length and width 9cm
Apologies for the mistake in the previous calculation. Let's recalculate with the correct dimensions:
Given:
Length (l) = 9cm
Width (w) = 9cm
Height (h) = 12cm
The volume of the container is given as 801.5cm³:
V = lwh
801.5 = 9 * 9 * 12
801.5 = 972
This is not equal to 801.5, so let's adjust the volume proportionally:
Adjusting the volume:
Adjusted volume = 801.5 * (972 / 801.5) = 972 cm³
Now that we have the correct volume, let's calculate the area of material needed to make the container:
1. Front and back faces:
Area = 2lw
Area = 2 * 9 * 12 = 216 cm²
2. Top and bottom faces:
Area = 2wh
Area = 2 * 9 * 12 = 216 cm²
3. Side faces:
Area = 2lh
Area = 2 * 9 * 12 = 216 cm²
Therefore, the total area of material needed to make the container is:
Total Area = 2lw + 2wh + 2lh
Total Area = 216 + 216 + 216
Total Area = 648 cm²
Therefore, the correct area of material needed to make the container with dimensions Length = 9cm, Width = 9cm, and Height = 12cm is 648 cm². Thank you for pointing out the mistake.
The correct answer is 529cm²
Apologies for the oversight in the previous calculation. Let's recalculate the area of material needed using the correct dimensions:
Given:
Length (l) = 9cm
Width (w) = 9cm
Height (h) = 12cm
The correct volume of the container is 801.5cm³:
V = lwh
801.5 = 9 * 9 * 12
801.5 = 972 cm³
Now, let's calculate the area of material needed to make the container using the correct dimensions:
1. Front and back faces:
Area = 2lw
Area = 2 * 9 * 12 = 216 cm²
2. Top and bottom faces:
Area = 2wh
Area = 2 * 9 * 12 = 216 cm²
3. Side faces:
Area = 2lh
Area = 2 * 9 * 12 = 216 cm²
Therefore, the total area of material needed to make the container is:
Total Area = 2lw + 2wh + 2lh
Total Area = 216 + 216 + 216
Total Area = 648 cm²
It seems that the calculated area is still 648cm² based on the given dimensions and volume. If there is a specific error in the calculation or additional information provided, please let me know so I can correct it.
The object is a combination of a cuboid and a triangular prism with a height of 12 cm and a width and length of 9cm. The volume is 850.5 (851) cm³. Find the area of material needed to make the container in cm²
To find the area of material needed to make the container, which is a combination of a cuboid and a triangular prism, with a height of 12 cm and a width and length of 9cm, and a volume of 851 cm³, we first need to determine the dimensions of the container.
Let's first determine the volume for each of the shapes separately and then combine them to match the total volume given:
1. Cuboid:
For the cuboid part with dimensions:
Length (l) = 9cm
Width (w) = 9cm
Height (h) = 12cm
The volume of the cuboid can be calculated as:
V_cuboid = l * w * h
V_cuboid = 9 * 9 * 12
V_cuboid = 972 cm³
2. Triangular prism:
The volume of a triangular prism is given by the formula V_prism = 0.5 * base * height * length. Since we know the height and the base (width), we can calculate the length of the base using the formula for the volume of a triangular prism:
V_prism = 0.5 * w * h * l
851 = 0.5 * 9 * 12 * l
851 = 54l
l = 851 / 54
l ≈ 15.75 cm
Now we can calculate the volume of the prism:
V_prism = 0.5 * 9 * 12 * 15.75
V_prism = 851.25 cm³
Total Volume:
Total volume = V_cuboid + V_prism
Total volume = 972 + 851.25
Total volume ≈ 1823.25 cm³
Since the total volume should be 851 cm³, the previously calculated area was incorrect. Let's find the correct area needed:
Now that we have the correct total volume, we can calculate the area of material needed:
The area of material needed would be the surface area of the cuboid and the triangular prism.
The surface area of the cuboid (including the base and top):
Area_cuboid = 2lw + 2wh + 2lh
Area_cuboid = 2(9*9) + 2(9*12) + 2(9*12)
Area_cuboid = 324 cm²
The surface area of the triangular prism (excluding the base):
Area_prism = l * (0.5 * w * h) + w * h + l * h
Area_prism = 15.75 * (0.5 * 9 * 12) + 9 * 12 + 15.75 * 12
Area_prism = 213.75 cm²
Total area of material needed:
Total Area = Area_cuboid + Area_prism
Total Area = 324 + 213.75
Total Area = 537.75 cm²
Therefore, the correct area of material needed to make the container with the given dimensions is approximately 537.75 cm². Thank you for providing the additional information to correct the calculation.
The correct answer is 529 cm²
I apologize for the error. Let's correct the calculation and find the area of material needed to make the container:
Given:
- Cuboid dimensions: Length (l) = 9cm, Width (w) = 9cm, Height (h) = 12cm
- Triangular prism height: 12cm
- Total volume of the container: 851 cm³
1. Cuboid Volume Calculation:
V_cuboid = l * w * h
V_cuboid = 9 * 9 * 12
V_cuboid = 972 cm³
2. Triangular Prism Volume Calculation:
Since the triangular prism is part of the container, we need to adjust the volume calculation based on the total volume given:
Total Volume = V_cuboid + V_prism
851 = 972 + V_prism
V_prism = 851 - 972
V_prism = -121 cm³
This indicates an error in the previous calculation. Let's correct the calculation for the triangular prism:
V_prism = 0.5 * base * height * length
- Base (Width in this case) = 9cm
- Height = 12cm
- Volume = 121cm³
Let's recalculate the volume using the corrected values:
Volume prism = 0.5 * 9 * 12 * l
121 = 54l
l = 121 / 54
l ≈ 2.24 cm
Now we correct the volume calculation for the triangular prism:
V_prism = 0.5 * 9 * 12 * 2.24
V_prism = 120.96 cm³
Now, let's calculate the correct area of material needed:
1. Surface Area of Cuboid:
Area_cuboid = 2lw + 2wh + 2lh
Area_cuboid = 2(9 * 9) + 2(9 * 12) + 2(9 * 12)
Area_cuboid = 162 + 216 + 216
Area_cuboid = 594 cm²
2. Surface Area of Triangular Prism (Including the triangular base):
The total surface area of a triangular prism should include the area of the triangular base plus the lateral area.
Area_prism = 3 * (0.5 * base * height) + (base * height)
Area_prism = 3 * (0.5 * 9 * 12) + (9 * 12)
Area_prism = 162 + 108
Area_prism = 270 cm²
Total Area of Material Needed:
Total Area = Area_cuboid + Area_prism
Total Area = 594 + 270
Total Area = 864 cm²
Therefore, the corrected area of material needed to make the container with the given dimensions is 864 cm².