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
wrong how da hell did you get that big of a number
I apologize for the mistake. Let's correct it.
The volume of the hexagonal prism can be calculated by finding the area of the hexagonal base and multiplying it by the height of the prism.
The formula for the area of a regular hexagon is: Area = (3√3 * side length^2) / 2
Given that the side length of the hexagon is 30 cm, we can calculate the area of the hexagonal base:
Area = (3√3 * 30^2) / 2
Area = (3√3 * 900) / 2
Area = (2598.076) / 2
Area ≈ 1299.038 cm^2
Now, we multiply the area of the hexagon by the height of the hexagonal prism (8 cm) to find the volume:
Volume = 1299.038 cm^2 * 8 cm
Volume ≈ 10392.3 cm^3
Therefore, the correct volume of the box is approximately 10392.3 cm^3.
still wrong
Apologies for the mistake in the previous calculations. Let's correct it.
The given hexagonal prism consists of a hexagonal base with sides of length 30 cm and height 8 cm.
To find the volume of the hexagonal prism, we need to first calculate the area of the hexagonal base using the formula:
Area = (3√3 * side length^2) / 2
Plugging in the values:
Area = (3√3 * 30^2) / 2
Area = (3√3 * 900) / 2
Area = (2700√3) / 2
Area = 1350√3 cm^2
Now, to find the volume of the hexagonal prism, we multiply the area of the base by the height:
Volume = 1350√3 cm^2 * 8 cm
Volume = 10800√3 cm^3
Using a calculator to find the approximate value:
Volume ≈ 18693.96 cm^3
Therefore, the correct volume of the box is approximately 18693.96 cm^3.
The volume of the hexagonal prism can be calculated by finding the area of the hexagonal base and multiplying it by the height of the prism.
The area of a regular hexagon can be calculated using the formula: Area = (3√3 * side length^2) / 2
In this case, the side length of the hexagon is 30 cm. So, the area of the hexagon is:
Area = (3√3 * 30^2) / 2
Area = (3√3 * 900) / 2
Area = (2598.76) / 2
Area = 1299.38 cm^2
Now, multiplying the area of the hexagon by the height of the hexagonal prism (8 cm), we get the volume of the prism:
Volume = 1299.38 cm^2 * 8 cm
Volume = 10394.4 cm3
Therefore, the volume of the box is 10394.4 cm3.