Question

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?

Answer 1

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

Answer 2

The relationship between the volumes of the two prisms is:

V2 = (27) * V1