Question

use the image to answer the question

image long description
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)
the volumes of the two figures have a ratio of ( 125:1 )
the volumes of the two figures have a ratio of ( 5:1 )
there is no scale factor stated for the volume.
the volumes of the two figures have a ratio of ( 25:1 )

Explanation:

Step1: Calculate the volume of Figure A

The base of the triangular prism in Figure A is a triangle with base \(b = 27.5\) ft and height \(h_{triangle}=27.5\) ft. The area of the triangular base \(B_A=\frac{1}{2}\times27.5\times27.5=\frac{756.25}{2}\) \(ft^{2}\). The length of the prism (height of the prism in the volume formula \(V = Bh\)) \(l_A = 55\) ft. So the volume \(V_A=B_A\times l_A=\frac{1}{2}\times27.5\times27.5\times55\).

Step2: Calculate the volume of Figure B

The base of the triangular prism in Figure B is a triangle with base \(b = 5.5\) ft and height \(h_{triangle}=5.5\) ft. The area of the triangular base \(B_B=\frac{1}{2}\times5.5\times5.5=\frac{30.25}{2}\) \(ft^{2}\). The length of the prism (height of the prism in the volume formula \(V = Bh\)) \(l_B=11\) ft. So the volume \(V_B=B_B\times l_B=\frac{1}{2}\times5.5\times5.5\times11\).

Step3: Find the ratio of \(V_A\) to \(V_B\)

\(\frac{V_A}{V_B}=\frac{\frac{1}{2}\times27.5\times27.5\times55}{\frac{1}{2}\times5.5\times5.5\times11}\)
Since \(\frac{27.5}{5.5} = 5\) and \(\frac{55}{11}=5\), then \(\frac{V_A}{V_B}=5\times5\times5=125\)

Answer:

The volumes of the two figures have a ratio of \(125:1\)