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
To find the volume of the box, we first need to find the volume of the hexagonal prism and then the volume of the triangular prism that is part of the box.
Volume of the hexagonal prism:
Base area of a hexagon = (3√3/2) * side length^2
Base area of the hexagonal prism = (3√3/2) * 30^2 = 783 cm^2
Volume of the hexagonal prism = base area * height = 783 cm^2 * 8 cm = 6264 cm^3
Volume of the triangular prism:
Base area of a triangle = 0.5 * base length * height
Base area of the triangular prism = 0.5 * 15 cm * 8 cm = 60 cm^2
Volume of the triangular prism = base area * height = 60 cm^2 * 8 cm = 480 cm^3
Total volume of the box = volume of hexagonal prism + volume of triangular prism = 6264 cm^3 + 480 cm^3 = 6744 cm^3
Therefore, the volume of the box is 6744 cm^3.
That answer is incorrect Use the image to answer the question.
An illustration shows a structure of a building shaped like an inverted letter upper L, formed by two rectangular perpendicular prisms to look like a two-winged building. The structure is 9 meters high. The horizontal rectangular prism has an overall length of 30 meters along the back edge. It has a width of 6 meters. Doors are drawn along the inside 24-meter length. The smaller perpendicular rectangular prism adjoins the horizontal prism along the right side and extends forward. It shows an inner length of 21 meters.
What is the total volume of this corner store?
(1 point)
m3
To find the total volume of the corner store formed by the two rectangular prisms, we first need to calculate the volume of each prism and then add them together.
1. Volume of the horizontal rectangular prism:
Volume = length * width * height
Volume = 30m * 6m * 9m = 1620 cubic meters
2. Volume of the smaller perpendicular rectangular prism:
Volume = length * width * height
Volume = 21m * 6m * 9m = 1134 cubic meters
Total volume of the corner store = Volume of horizontal prism + Volume of smaller prism
Total volume = 1620 cubic meters + 1134 cubic meters = 2754 cubic meters
Therefore, the total volume of the corner store is 2754 cubic meters.