Question

Question
Use the image to answer the question.

2 similarly shaped wedge polyhedrons labeled Figure upper A and Figure upper B.

Image Long DescriptionFigure upper A shows a triangle labeled with height of 27.5 feet and base of 27.5 feet. A face is labeled with a length of 55 feet. Figure upper B shows a triangle labeled with height of 5.5 feet and base of 5.5 feet. A face is labeled with a length of 11 feet.

The volume of a triangular prism with the area of the triangular base B and height h can be found using the formula V=Bh
. Calculate and compare the volume of the two figures in the image. Choose which statement is true.

(1 point)
Responses

Answer 1

Compute base area B = 1/2·(base)(height) and V = B·length.

Figure A:
B_A = 1/2·27.5·27.5 = 378.125 ft^2
V_A = 378.125·55 = 20,796.875 ft^3

Figure B:
B_B = 1/2·5.5·5.5 = 15.125 ft^2
V_B = 15.125·11 = 166.375 ft^3

Ratio: V_A / V_B = 20,796.875 / 166.375 = 125. So Figure A’s volume is 125 times the volume of Figure B (equivalently V_A = 125·V_B).