Question

A) You are designing a rectangular keychain on a 3D printer. Your outer prism has dimensions of 50 mm by 20 mm by 5 mm and your inner prism (hole) has dimensions of 46 mm by 16 mm by 3 mm. What is the volume remaining of your outer prism once the hole is applied? Show your mathematical steps for calculating the remaining volume here.B) Briefly describe the 2-dimensional shapes that are present in your keychain:C) Briefly describe the 3-dimensional shapes that are present in your keychain:(I've attached 2 images to better help your understanding of the question. The first is the actual model of the keychain. The second image is the keychain drawn (not to scale) with dimensions of both the hole and outer prism. Sorry for the confusion! Thank you so so much for your help!)

Answer 1

Step-by-step explanation

The outer prism has volume:

`V_1=50\text{ }mm*20\text{ }mm*5\text{ }mm=5000mm^3`

And the inner prism has volume:

`V_2=46mm*16mm*3mm=2208mm^3`

The volume remaining of outer prism once the hole is applied is:

`V=V_1-V_2=5000mm^3-2208mm^3=2792mm^3`

The figure is mostly made up of rectangles (2-dimensions), which form parallelepipeds (3-dimensions).