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
The main part of the box is a hexagonal prism with a height of 8 cm and two longer parallel sides measuring 30 cm each. To find the volume of the hexagonal prism, we use the formula:
Volume = Area of base x height
The base of the hexagonal prism is a regular hexagon, which can be divided into 6 equilateral triangles. Each equilateral triangle has a base of 30 cm and a height of 15 cm (half of the dashed line measurement).
Area of one equilateral triangle = 0.5 x base x height
Area of one equilateral triangle = 0.5 x 30 cm x 15 cm
Area of one equilateral triangle = 225 cm^2
Since there are 6 identical triangles, the total area of the base of the hexagonal prism is 6 x 225 cm^2 = 1350 cm^2.
Now, we can find the volume of the hexagonal prism:
Volume = 1350 cm^2 x 8 cm
Volume = 10800 cm^3
The triangular prism formed by the dashed line has a base area of 0.5 x 15 cm x 8 cm = 60 cm^2.
To find the total volume of the box, we add the volume of the hexagonal prism and the triangular prism:
Total volume = 10800 cm^3 + 60 cm^3
Total volume = 10860 cm^3
Therefore, the volume of the box is 10860 cm^3.