Question

7. Filament for 3D printing is sold in spools that contain something shaped like a wire of diameter 3 mm. John wants to make 3D printings of a cone with radius 2 cm and height 3 cm. The length of the filament is 25 meters. About how many cones can John make?

Answer 1

14 cones

Explanation:

First we need to discover the total volume of the wire that we have available to make the cones, so we treat it as a long circular prism, with radios of 1,5 mm and 25,000 milimeters height:

`Volume=\pi r^(2)*h\\Volume=\pi (1.5)^(2) *25,000\\Volume= 176,635 mm^(3)`

Now we just have to calculate the volume of the cone:

`Volume*cone=\pi r^(2)(h)/(3)  \\Volume=\pi 20^(2)(30)/(3)  \\Volume= 12,566 mm^(3)`

And finally we just have to divide the volume available between the volume necessary for each cone:

176,635/12,566=14.05