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
To find the total volume of the restaurant with an enclosed porch shown in the diagram, we need to calculate the volume of the two rectangular prisms separately 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 yd^3
Volume of the larger rectangular prism:
Volume = length x width x height
Volume = 32 yards x 16 yards x 8 yards (since the total depth is 15 yards, and the smaller prism is 5 yards deep)
Volume = 4,096 yd^3
Total volume = Volume of smaller prism + Volume of larger prism
Total volume = 960 yd^3 + 4,096 yd^3
Total volume = 5,056 yd^3
Therefore, the total volume of the restaurant with an enclosed porch shown in the diagram is 5,056 yd^3.