Rosario draws the right triangular prism shown here and calculates the volume. She then draws a second right triangular prism in which the dimensions are tripled. What is the relationship between the volumes of the two prisms?

The volume of the original prism is given by:

V1 = (1/2) * (b) * (h) * (H)

Where,

b: base of the triangle

h: height of the triangle

H: prism height

The volume of the prism with new dimensions is:

V2 = (1/2) * (3b) * (3h) * (3H)

Rewriting:

V2 = (3 * 3 * 3) * (1/2) * (b) * (h) * (H)

V2 = (27) * (1/2) * (b) * (h) * (H)

V2 = (27) * V1

Answer:

The relationship between the volumes of the two prisms is:

V2 = (27) * V1