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?
_m^3
The total volume of the corner store can be calculated by finding the volume of each rectangular prism separately and then adding them together.
Volume of the horizontal rectangular prism:
Length = 30 meters
Width = 6 meters
Height = 9 meters
Volume = Length x Width x Height
Volume = 30m x 6m x 9m
Volume = 1620 cubic meters
Volume of the smaller perpendicular rectangular prism:
Length = 21 meters (inner length)
Width = 6 meters (width of the horizontal prism)
Height = 9 meters
Volume = Length x Width x Height
Volume = 21m x 6m x 9m
Volume = 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
Total volume = 2754 cubic meters
Therefore, the total volume of the corner store is 2754 cubic meters.
use the image to answer the question.
An illustration shows a rectangular prism joined two triangular prisms on either side. The illustration shows two identical triangular prisms, each with one side attached to the length of the rectangular prism. The sides attached to the rectangular prism are oriented such that the triangular prisms are mirror images of one another. The length of the rectangular prism is 14 centimeters. The width and the height are 5 centimeters and 4 centimeters respectively. The distance from the apex of the triangular prism to the base is 6 centimeters.
solve for the volume of the composite figure
616 cm^3
952 cm^3
154 cm^3
448 cm^3
To find the volume of the composite figure, we first need to calculate the volume of the rectangular prism and the volume of one triangular prism, then multiply the triangular prism's volume by 2 since there are two identical triangular prisms.
Volume of the rectangular prism:
Length = 14 cm
Width = 5 cm
Height = 4 cm
Volume = Length x Width x Height
Volume = 14 cm x 5 cm x 4 cm
Volume = 280 cm^3
Volume of one triangular prism:
Base = 5 cm
Height from base to apex = 6 cm
Height = 4 cm
Volume = (1/2) x Base x Height x Height from base to apex
Volume = (1/2) x 5 cm x 4 cm x 6 cm
Volume = 60 cm^3
Since there are two identical triangular prisms, the total volume contributed by both triangular prisms is 2 x 60 cm^3 = 120 cm^3.
Total volume of the composite figure = Volume of rectangular prism + Volume of two triangular prisms
Total volume = 280 cm^3 + 120 cm^3
Total volume = 400 cm^3
Therefore, the volume of the composite figure is 400 cm^3.
thats not even an answer
I apologize for the error in my previous response. Let's calculate the correct volume of the composite figure considering the structure shown in the image.
The composite figure consists of a rectangular prism and two identical triangular prisms attached to its sides.
Volume of the rectangular prism:
Length = 14 cm
Width = 5 cm
Height = 4 cm
Volume = Length x Width x Height
Volume = 14 cm x 5 cm x 4 cm
Volume = 280 cm^3
Volume of one triangular prism:
Base = 5 cm
Height from base to apex = 6 cm
Height = 4 cm
Volume = (1/2) x Base x Height x Height from base to apex
Volume = (1/2) x 5 cm x 4 cm x 6 cm
Volume = 60 cm^3
Since there are two identical triangular prisms, the total volume contributed by both triangular prisms is 2 x 60 cm^3 = 120 cm^3.
Total volume of the composite figure = Volume of rectangular prism + Volume of two triangular prisms
Total volume = 280 cm^3 + 120 cm^3
Total volume = 400 cm^3
Therefore, the correct volume of the composite figure is 400 cm^3.