Volume of Cylinders and Composite 3D Figures Practice
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Question
Use the image to answer the question.
An illustration shows a hexagonal prism with the label Choosy Cheesy on the top surface. The height of the hexagonal prism is 8 centimeters. The two longer parallel sides of the hexagonal prism each measure 30 centimeters in length. One end of the prism is marked with a dashed line measuring 15 centimeters across, joining the two opposite vertices of the parallel edges, forming a triangular prism with a perpendicular measure of 8 centimeters.
A sample of gourmet cheeses came in this box. What is the volume of the box?
(1 point)
cm3
This isn't the answer
I apologize for the mistake in my previous response. Let me correct it:
To find the volume of the hexagonal prism, you first need to find the area of the base (the hexagon) and then multiply it by the height.
The formula for the area of a regular hexagon is: A = (3√3 * s^2) / 2, where s is the length of one side of the hexagon.
Given that the two longer parallel sides of the hexagonal prism each measure 30 cm, those are the sides of the regular hexagon, so s = 30 cm.
A = (3√3 * 30^2) / 2
A = (3 * 900 * √3) / 2
A = 1350√3 cm^2
Now that we have the area of the base, we can calculate the volume of the hexagonal prism:
Volume = base area * height
Volume = 1350√3 cm^2 * 8 cm
Volume = 10800√3 cm^3
So, the volume of the box (hexagonal prism) is 10800√3 cm^3.
THAT AIN'T THE ANSWER!!!!
I apologize for the mistake. Let's correct the calculation:
The hexagonal prism can be divided into a rectangular prism and two triangular prisms.
1. Calculate the volume of the rectangular prism:
Base area = 30 cm * 15 cm = 450 cm^2
Volume of the rectangular prism = Base area * height = 450 cm^2 * 8 cm = 3600 cm^3
2. Calculate the volume of one of the triangular prisms:
Base area = (1/2) * 15 cm * 8 cm = 60 cm^2
Volume of one triangular prism = Base area * height = 60 cm^2 * 15 cm = 900 cm^3
Since there are two triangular prisms, the total volume of both is 900 cm^3 * 2 = 1800 cm^3
3. Add the volumes of the rectangular prism and the two triangular prisms together:
Volume of the hexagonal prism = 3600 cm^3 (rectangular prism) + 1800 cm^3 (two triangular prisms) = 5400 cm^3
Therefore, the volume of the box (hexagonal prism) is 5400 cm^3.
Ain't the aNSWER
I apologize for the errors in my previous responses. Let's recalculate the volume of the hexagonal prism.
Given:
- Dimensions of the hexagonal prism:
- Base: 30 cm (longer side) and 15 cm (dashed line forming a side of the triangle)
- Height of the prism: 8 cm
To find the volume of the hexagonal prism, we need to calculate the area of the base (hexagon) and then multiply it by the height of the prism.
1. Calculate the area of the hexagon base:
Area of hexagon = 6 * (1/2) * base * apothem
Apothem of the hexagon = side length of the triangle = 15 cm (since the dashed line forms a side of the triangle)
Area = 6 * (1/2) * 30 cm * 15 cm = 270 * 15 = 4050 cm^2
2. Calculate the volume of the hexagonal prism:
Volume = Base area * height
Volume = 4050 cm^2 * 8 cm = 32400 cm^3
Therefore, the volume of the hexagonal prism (box) is 32400 cm^3.
too high
I apologize for the mistakes in the previous responses. Let's correct the calculation for the volume of the hexagonal prism.
Given:
- Longer side length of the hexagonal base = 30 cm
- Side length of the triangle forming the prism = 15 cm
- Height of the hexagonal prism = 8 cm
To find the volume of the hexagonal prism, we first need to calculate the area of the hexagonal base.
1. Calculate the area of the hexagonal base:
Area of hexagon = 6 * (1/2) * base * apothem
Apothem of the hexagon = side length of the triangle = 15 cm
Area = 6 * (1/2) * 30 cm * 15 cm = 6 * 15 * 15 = 1350 cm^2
2. Calculate the volume of the hexagonal prism:
Volume = Base area * height
Volume = 1350 cm^2 * 8 cm = 10800 cm^3
Therefore, the volume of the hexagonal prism (box) is 10800 cm^3.
Use the image to answer the question.
An illustration shows a hexagonal prism with the label Choosy Cheesy on the top surface. The height of the hexagonal prism is 8 centimeters. The two longer parallel sides of the hexagonal prism each measure 30 centimeters in length. One end of the prism is marked with a dashed line measuring 15 centimeters across, joining the two opposite vertices of the parallel edges, forming a triangular prism with a perpendicular measure of 8 centimeters.
A sample of gourmet cheeses came in this box. What is the volume of the box?
To find the volume of the box (hexagonal prism), we need to calculate the volume of the entire hexagonal prism by considering it as a combination of a rectangular prism and two triangular prisms.
1. Calculate the volume of the rectangular prism part of the hexagonal prism:
The two longer parallel sides of the hexagonal prism form a rectangular base.
- The base area of the rectangular part = length * width = 30 cm * 15 cm = 450 cm^2
- The height of the entire prism = 8 cm
- Volume of the rectangular prism part = base area * height = 450 cm^2 * 8 cm = 3600 cm^3
2. Calculate the volume of one of the triangular prisms:
The dashed line across one end forms a base of a triangular prism.
- The base area of one triangular prism = (1/2) * base * height = (1/2) * 15 cm * 8 cm = 60 cm^2
- The height of the entire prism = 8 cm
- Volume of one triangular prism = base area * height = 60 cm^2 * 8 cm = 480 cm^3
Since there are two triangular prisms, the total volume of both = 480 cm^3 * 2 = 960 cm^3
3. Add the volume of the rectangular prism part and the total volume of the two triangular prisms:
Total volume of the hexagonal prism (box) = 3600 cm^3 (rectangular part) + 960 cm^3 (trigonal prism parts) = 4560 cm^3
Therefore, the volume of the box (hexagonal prism) is 4560 cm^3.