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 doubled. What is the relationship between the volumes of the two prisms?
The volume of a rectangular triangular prism is given by: V = (1/2) * (b) * (h) * (l) Where, b: base of the triangle h: height of the triangle l: prism length The volume of the prism when the dimensions are modified is: V '= (1/2) * (2b) * (2h) * (2l) V '= (8) * (1/2) * (b) * (h) * (l) V '= 8 * V The relationship between both volumes is: V '/ V = 8 Answer: The relationship between the volumes of the two prisms is: V '/ V = 8 Equivalently: V '= 8 * V
