Question

Figure 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.

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
𝑉
=
𝐵
ℎ
. Calculate and compare the volume of the two figures in the image. Choose which statement is
The volumes of the two figures have a ratio of 25:1
25
:
1
.
The volumes of the two figures have a ratio of ratio of 25 to 1 .

There is no scale factor stated for the volume.
There is no scale factor stated for the volume.

The volumes of the two figures have a ratio of 125:1
125
:
1
.
The volumes of the two figures have a ratio of ratio of 125 to 1 .

The volumes of the two figures have a ratio of 5:1
5
:
1
.
The volumes of the two figures have a ratio of ratio of 5 to 1 .

Answer 1

Scale factor for lengths = 27.5/5.5 = 55/11 = 5. Volume scales by the cube of the linear scale factor, so volume ratio = 5^3 = 125.

Thus the volumes have ratio 125 : 1 (large : small).