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.
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)
THE BASE AREA IS 30
5 answers
no
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.
nope
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.
5 answers