Question

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.

Answer 1

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

Answer 2

Answer:

1. Yes, they are similar because their corresponding sides are proportional.

2. The prism with Triangle DEF as the base will have the greater volume. The prism with the base as Triangle DEF will have a volume 1.44 times greater than the prism with Triangle ABC as the base.

Step-by-step explanation:

1. 48/40= 1.2 and 36/30= 1.2

2. The volume of a prism is the area of the base times the height. In our case, the base is a triangle so use the formula for area of a triangle to find the area of the base. A= b x h x 1/2 (where b is the base length and h is the height of the triangle) First find the volumes.

For the prism with base ABC: 30 x 40 x 1/2 = 600

V=600 x h

For the prism with base DEF: 36 x 48 x 1/2 = 864

V=864 x h

Now that we have the volumes we can see that the prism with base DEF has a greater volume. To find how much greater we would disregard the height of the prism for now and...

864/600=1.44

(I know you might want to subtract rather than divide because that's what I did for my assignment. However, I got it wrong for some reason and my teacher said that instead of 864-600 I needed to do 864/600. I'm not sure why....but hopefully I helped in some way! )