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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?

Answer :

carlosego
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

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