To find the total volume of the composite figure, we first need to find the volume of each rectangular prism separately, and then add them together.
Volume of the smaller rectangular prism:
V = l x w x h
V = 32 yards x 5 yards x 6 yards
V = 960 cubic yards
Volume of the larger rectangular prism:
V = l x w x h
V = 32 yards x 15 yards x 16 yards
V = 7,680 cubic yards
Total volume of the composite figure:
960 cubic yards + 7,680 cubic yards = 8,640 cubic yards
So, the total volume of the restaurant with an enclosed porch shown in the diagram is 8,640 yd.3.
Volume of Composite 3D Figures Quick Check
4 of 54 of 5 Items
Question
Use the image to answer the question.
A 3-dimensional illustration shows two horizontal rectangular prisms, with the smaller one adjoined along the front face of the larger one, to look like steps. Edges that are not visible are drawn with dashed lines. The rectangular prism in front is smaller than the one in the back. The length of both the prisms is 32 yards. The smaller rectangular prism is 6 yards high and 5 yards deep. The larger rectangular prism is 16 yards high. The total combined depth of the two prisms is 15 yards.
What is the total volume of the restaurant with an enclosed porch shown in the diagram?
(1 point)
Responses
8,640 yd.3
8,640 yd. cubed
4,160 yd.3
4,160 yd. cubed
6,080 yd.3
6,080 yd. cubed
5,070 yd.3
3 answers
wrong
I apologize for the error. Let's correct it by recalculating the total volume of the composite figure.
Volume of the smaller rectangular prism:
V = l x w x h
V = 32 yards x 5 yards x 6 yards
V = 960 cubic yards
Volume of the larger rectangular prism:
Since the total combined depth of the two prisms is 15 yards and the smaller prism has a depth of 5 yards, the depth of the larger prism would be:
15 yards - 5 yards = 10 yards
V = l x w x h
V = 32 yards x 10 yards x 16 yards
V = 5,120 cubic yards
Total volume of the composite figure:
960 cubic yards (smaller prism) + 5,120 cubic yards (larger prism) = 6,080 cubic yards
Therefore, the total volume of the restaurant with an enclosed porch shown in the diagram is 6,080 yd.3. Thank you for your patience.
Volume of the smaller rectangular prism:
V = l x w x h
V = 32 yards x 5 yards x 6 yards
V = 960 cubic yards
Volume of the larger rectangular prism:
Since the total combined depth of the two prisms is 15 yards and the smaller prism has a depth of 5 yards, the depth of the larger prism would be:
15 yards - 5 yards = 10 yards
V = l x w x h
V = 32 yards x 10 yards x 16 yards
V = 5,120 cubic yards
Total volume of the composite figure:
960 cubic yards (smaller prism) + 5,120 cubic yards (larger prism) = 6,080 cubic yards
Therefore, the total volume of the restaurant with an enclosed porch shown in the diagram is 6,080 yd.3. Thank you for your patience.