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)
a
cm3
To find the volume of the box, we first need to calculate the volume of the hexagonal prism and the volume of the triangular prism, and then add them together.
Volume of the hexagonal prism:
Base Area = 6 * ((1/2)*15*8) = 6 * 60 = 360 cm^2
Volume = Base Area * Height = 360 * 8 = 2880 cm^3
Volume of the triangular prism:
Base Area = (1/2) * 15 * 8 = 60 cm^2
Volume = Base Area * Height = 60 * 30 = 1800 cm^3
Total Volume = Volume of hexagonal prism + Volume of triangular prism
Total Volume = 2880 + 1800 = 4680 cm^3
Therefore, the volume of the box is 4680 cm^3.
wrong
Apologies for the mistake. Let's correct it:
To find the volume of the hexagonal prism, we need to calculate the area of the hexagon and then multiply by the height.
Area of the hexagon = (3√3 * (side length)^2) / 2
Area of the hexagon = (3√3 * 15^2) / 2 = 487.5 cm^2
Volume of the hexagonal prism = Area of the hexagon * height
Volume of the hexagonal prism = 487.5 * 8 = 3900 cm^3
Next, we need to calculate the volume of the triangular prism.
Area of the triangle = (1/2) * base length * height
Area of the triangle = (1/2) * 15 * 8 = 60 cm^2
Volume of the triangular prism = Area of the triangle * length
Volume of the triangular prism = 60 * 30 = 1800 cm^3
Total volume of the box = Volume of the hexagonal prism + Volume of the triangular prism
Total volume = 3900 + 1800 = 5700 cm^3
Therefore, the volume of the box is 5700 cm^3.
A sample of gourmet cheeses came in this box. What is the volume of the box?
(1 point)
a
cm3
The correct answer is:
a) 5700 cm3
recalculate
Apologies for the mistake. Let's recalculate the volume of the box:
Volume of the hexagonal prism:
Base Area = 6 * ((1/2) * 15 * 8) = 6 * 60 = 360 cm^2
Volume = Base Area * Height = 360 * 8 = 2880 cm^3
Volume of the triangular prism:
Base Area = (1/2) * 15 * 8 = 60 cm^2
Volume = Base Area * Length = 60 * 30 = 1800 cm^3
Total Volume = Volume of hexagonal prism + Volume of triangular prism
Total Volume = 2880 + 1800 = 4680 cm^3
Therefore, the volume of the box is 4680 cm^3.