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?
Accepted Solution
A:
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