Question

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

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

The volumes of the two figures have a ratio of 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 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.

Answer 1

125:1

Reason: If the prisms are similar with linear scale factor k = 5, the base area scales by k^2 and the prism height by k, so the volume scales by k^3 = 5^3 = 125. Thus the volumes are in ratio 125:1.