To find the volume of the hexagonal prism box, we need to first calculate the area of the hexagonal base.
Since a hexagon can be divided into 6 equilateral triangles, we can calculate the area of each triangle using the formula for the area of an equilateral triangle:
Area = (base x height) / 2
Area of one equilateral triangle = (30 x 8) / 2 = 120 square centimeters
Since the hexagon has 6 of these equilateral triangles, the total base area = 6 x 120 = 720 square centimeters
Now that we have the base area, we can calculate the volume of the hexagonal prism:
Volume = base area x height
Volume = 720 x 8 = 5760 cubic centimeters
Therefore, the volume of the hexagonal prism box is 5760 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?
THE BASE AREA IS 30
5 answers
nope
I apologize for the incorrect answer. Let's try to calculate the correct volume of the box.
The base of the hexagonal prism is a regular hexagon, which can be divided into six equilateral triangles. Each side of the hexagon has a length of 30 cm. Using the formula for the area of a regular hexagon, we can find the area of one equilateral triangle:
Area of one equilateral triangle = (sqrt(3) / 4) x side^2
Area of one equilateral triangle = (sqrt(3) / 4) x 30^2
Area of one equilateral triangle = (sqrt(3) / 4) x 900
Area of one equilateral triangle = (sqrt(3) / 4) x 900
Area of one equilateral triangle = (30sqrt(3)) / 2
Area of one equilateral triangle = 15sqrt(3)
Since the hexagon has 6 of these equilateral triangles, the total base area = 6 x 15sqrt(3) = 90sqrt(3) square centimeters
Now that we have the base area, we can calculate the volume of the hexagonal prism:
Volume = base area x height
Volume = 90sqrt(3) x 8
Volume = 720sqrt(3) cubic centimeters
Therefore, the volume of the hexagonal prism box is 720sqrt(3) cubic centimeters.
The base of the hexagonal prism is a regular hexagon, which can be divided into six equilateral triangles. Each side of the hexagon has a length of 30 cm. Using the formula for the area of a regular hexagon, we can find the area of one equilateral triangle:
Area of one equilateral triangle = (sqrt(3) / 4) x side^2
Area of one equilateral triangle = (sqrt(3) / 4) x 30^2
Area of one equilateral triangle = (sqrt(3) / 4) x 900
Area of one equilateral triangle = (sqrt(3) / 4) x 900
Area of one equilateral triangle = (30sqrt(3)) / 2
Area of one equilateral triangle = 15sqrt(3)
Since the hexagon has 6 of these equilateral triangles, the total base area = 6 x 15sqrt(3) = 90sqrt(3) square centimeters
Now that we have the base area, we can calculate the volume of the hexagonal prism:
Volume = base area x height
Volume = 90sqrt(3) x 8
Volume = 720sqrt(3) cubic centimeters
Therefore, the volume of the hexagonal prism box is 720sqrt(3) cubic centimeters.
not right
Let's try to calculate the volume of the hexagonal prism box again.
The base of the hexagonal prism is a regular hexagon, which can be divided into 6 equilateral triangles. Each side of the hexagon has a length of 30 cm. Using the formula for the area of an equilateral triangle:
Area of one equilateral triangle = (√3 / 4) x side^2
Area of one equilateral triangle = (√3 / 4) x 30^2
Area of one equilateral triangle = (√3 / 4) x 900
Area of one equilateral triangle = (30√3) / 2
Area of one equilateral triangle = 15√3 square centimeters
Since the hexagon has 6 of these equilateral triangles, the total base area = 6 x 15√3 = 90√3 square centimeters
Now that we have the base area, we can calculate the volume of the hexagonal prism:
Volume = base area x height
Volume = 90√3 x 8
Volume = 720√3 cubic centimeters
Therefore, the volume of the hexagonal prism box is 720√3 cubic centimeters.
The base of the hexagonal prism is a regular hexagon, which can be divided into 6 equilateral triangles. Each side of the hexagon has a length of 30 cm. Using the formula for the area of an equilateral triangle:
Area of one equilateral triangle = (√3 / 4) x side^2
Area of one equilateral triangle = (√3 / 4) x 30^2
Area of one equilateral triangle = (√3 / 4) x 900
Area of one equilateral triangle = (30√3) / 2
Area of one equilateral triangle = 15√3 square centimeters
Since the hexagon has 6 of these equilateral triangles, the total base area = 6 x 15√3 = 90√3 square centimeters
Now that we have the base area, we can calculate the volume of the hexagonal prism:
Volume = base area x height
Volume = 90√3 x 8
Volume = 720√3 cubic centimeters
Therefore, the volume of the hexagonal prism box is 720√3 cubic centimeters.