3. A sculptor is planning to make two triangular prisms out of steel. The sculptor will use for the bases of one prism and for the bases of the other prism. (a) Is similar to ? Explain. (b) Suppose the sculptor makes both prisms with the same height. Which prism will have a greater volume? How many times greater? Show your work.

1.  Yes, the are similar because if you set up a proportion for the sides of the triangles and cross-multiply, the values are the same: 40/48 = 30/36 If you cross-multiply you get 1,440 both ways 2.  Volume of the first prism:   V = (1/2)bhthp V = (1/2)(30)(40)hp V = 600hp