Use the image to answer the question.
the angles are 32 yd, 16 yd, 15 yd, 6 yd, and 5 yd.
What is the total volume of the restaurant with an enclosed porch shown in the diagram?
A. 8,640 yd.^3
B. 5,070 yd.^3
C. 6,080 yd.^3
D. 4,160 yd.^3
To find the volume of the restaurant with an enclosed porch, we need to calculate the volume of each individual shape and then add them together.
1. Rectangle with length 16 yd and width 32 yd:
Volume = length x width x height = 16 yd x 32 yd x 6 yd = 3072 yd^3
2. Triangle with base 15 yd and height 6 yd:
Volume = 0.5 x base x height x height = 0.5 x 15 yd x 6 yd x 6 yd = 270 yd^3
3. Trapezoid with bases 15 yd and 5 yd, and height 6 yd:
Volume = 0.5 x (base1 + base2) x height x height = 0.5 x (15 yd + 5 yd) x 6 yd x 6 yd = 180 yd^3
Adding the volumes of the three shapes together:
3072 yd^3 + 270 yd^3 + 180 yd^3 = 3522 yd^3
Therefore, the total volume of the restaurant with the enclosed porch shown in the diagram is 3522 yd^3.
None of the answer choices match this calculation, so it seems like there may be an error in the information provided or in the drawing.
choose one that is close to the correct answer
In that case, the closest answer choice to the calculated total volume would be:
C. 6,080 yd^3
Although it is not an exact match, it is the closest option to the calculated volume of 3522 yd^3.