We have the volume of the original prism is: V = (l) * (w) * (t) where, l = long, w: width t: depth For this case we can see that the original rectangular prism is dilated by a factor of 3 V = (3l) * (3w) * (3t) V = (l) * (w) * (t) * (3) * (3) * (3) V = (60) * (27) V = 1620 cm ^ 3 answer the volume of the larger rectangular prism is 1620 cm ^ 3
If two solids are similar the ratio of the corresponding sides is called the linear scale factor while the ratio of the areas is called the area scale factor and the ratio of their volumes is the volume scale factor. v.s.f = (l.s.f)³ in this case, the l.s.f = 5/15 = 1/3 therefore, the V.S.F = (1/3)³ = 1/27 Thus the volume of the larger prism = 60 ×27 = 1620 cm³
