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
6,080 yd.3
6,080 yd. cubed
5,070 yd.3
5,070 yd. cubed
4,160 yd.3
4,160 yd. cubed
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To find the total volume of the two rectangular prisms, we need to calculate the volume of each and then add them together.
Volume of the smaller rectangular prism:
Volume = length x width x height
Volume = 32 yards x 5 yards x 6 yards
Volume = 960 cubic yards
Volume of the larger rectangular prism:
Volume = length x width x height
Volume = 32 yards x width x 16 yards
Since the total depth is 15 yards, we can subtract the depth of the smaller prism (5 yards) from 15 yards to get the width of the larger prism:
Width = 15 yards - 5 yards
Width = 10 yards
Volume = 32 yards x 10 yards x 16 yards
Volume = 5,120 cubic yards
Total volume of the restaurant with an enclosed porch:
Total volume = volume of smaller prism + volume of larger prism
Total volume = 960 cubic yards + 5,120 cubic yards
Total volume = 6,080 cubic yards
Therefore, the total volume of the restaurant with an enclosed porch shown in the diagram is 6,080 yd.3.