Question

se 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)

Answer 1

Compute each triangular prism's volume V = (1/2 · base · height) · length.

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

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

Comparison:
27.5/5.5 = 55/11 = 5, so linear scale factor = 5 and volume scale factor = 5^3 = 125.
Thus V_A = 125 · V_B (20,796.875 ft^3 is 125 times 166.375 ft^3).