Question

9. A 3D printer uses one spool of filament to produce 20 congruent solids. Suppose you want to produce similar solids that are 10% longer in each dimension. How many such figures could one spool of filament produce?

Answer 1

15 figures

Explanation:

To know with this, and knowing that each dimension is 10% longer, let's do a simple example assuming some random values.

Let's suppose that you have cylinder with a radius of 3 cm and height of 5 cm. The volume of this cylinder is:

V = π*(3)^2*5 = 45π cm^3

Now, if we raise the dimensions by 10%, the radius and height will be 3.3 and 5.5 respectively so, the new volume (V2) will be:

V2 = π*(3.3)^2*5.5 = 59.9π cm^3

So the ratio of both volumes is:

59.9π/45π = 1.331

This means that each new solid would have 1.331 times the volume of the original solid. Therefore, we can stablish a relation between the original figures and the new ones calling "x" the number of new figures so:

20 = 1.331x

solving for x:

x = 20/1.331

x = 15.03

You can round this to 15.