Question
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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)
THE BASE AREA IS 30
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)
THE BASE AREA IS 30
Answers
Answer
no
Answer
nope
Answered by
GPT 3.5
2 * ((1/2 * 15) * 8) = 240 square centimeters
The volume is base area times height:
240 * 8 = 1920 cubic centimeters.
The volume of the box is 1920 cubic centimeters.
The volume is base area times height:
240 * 8 = 1920 cubic centimeters.
The volume of the box is 1920 cubic centimeters.
Answered by
GPT 3.5
I apologize for the mistake in my previous response. Let me correct it.
The base of the hexagonal prism is a hexagon with a side length of 30 cm, which can be split into 6 equilateral triangles.
Area of an equilateral triangle with side length 30 cm = (√3/4) * side^2
Therefore, area of one equilateral triangle = (√3/4) * 30^2 = 15√3 * 30 cm^2
Area of the hexagonal base = 6 * 15√3 * 30 cm^2 = 270√3 cm^2
Now, we can find the volume of the prism by multiplying the base area by the height.
Volume = base area * height
Volume = 270√3 cm^2 * 8 cm = 2160√3 cm^3
Therefore, the volume of the box is 2160√3 cubic centimeters.
The base of the hexagonal prism is a hexagon with a side length of 30 cm, which can be split into 6 equilateral triangles.
Area of an equilateral triangle with side length 30 cm = (√3/4) * side^2
Therefore, area of one equilateral triangle = (√3/4) * 30^2 = 15√3 * 30 cm^2
Area of the hexagonal base = 6 * 15√3 * 30 cm^2 = 270√3 cm^2
Now, we can find the volume of the prism by multiplying the base area by the height.
Volume = base area * height
Volume = 270√3 cm^2 * 8 cm = 2160√3 cm^3
Therefore, the volume of the box is 2160√3 cubic centimeters.
Answered by
GPT 3.5
I apologize for the errors in my previous responses. Let me calculate the volume correctly.
The base of the hexagonal prism is a hexagon with a side length of 30 cm, which can be split into 6 equilateral triangles.
Area of an equilateral triangle with side length 30 cm = (√3/4) * side^2
Therefore, area of one equilateral triangle = (√3/4) * 30^2 = 225√3 cm^2
Area of the hexagonal base = 6 * 225√3 cm^2 = 1350√3 cm^2
Now, we can find the volume of the prism by multiplying the base area by the height.
Volume = base area * height
Volume = 1350√3 cm^2 * 8 cm = 10800√3 cm^3
Therefore, the volume of the box is 10800√3 cubic centimeters.
The base of the hexagonal prism is a hexagon with a side length of 30 cm, which can be split into 6 equilateral triangles.
Area of an equilateral triangle with side length 30 cm = (√3/4) * side^2
Therefore, area of one equilateral triangle = (√3/4) * 30^2 = 225√3 cm^2
Area of the hexagonal base = 6 * 225√3 cm^2 = 1350√3 cm^2
Now, we can find the volume of the prism by multiplying the base area by the height.
Volume = base area * height
Volume = 1350√3 cm^2 * 8 cm = 10800√3 cm^3
Therefore, the volume of the box is 10800√3 cubic centimeters.
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