ISU Artifact - Part A

Volume Relationships

Volume is the amount of space occupied or enclosed by a 3-dimensional object.

• The volume of a prism can be found using the formula: lwh
  Practice with the Python Program below:
  
  "What's the volume of a prism with length (6), width(5), and height (10)?:"


• The volume of a pyramid can be found using the formula: 1/3(lwh)
  Practice with the Python Program below:
  
  "What's the volume of a pyramid with length (5), width(9), and height (2)?:"


• The volume of a cylinder can be found using the formula: πr^2h
  Practice with the Python Program below:
  
  "What's the volume of a cylinder with radius (5), and height(9)? Use 3.14 for π and round to nearest tenth:"


• The volume of a cone can be found using the formula: 1/3 (πr^2h)
  Practice with the Python Program below:
  
  "What's the volume of a cone with radius (4), and height(10)? Use 3.14 for π and round to nearest tenth:"

Summative code that lets you choose what you want to find:

Measurement Calculations in Three Dimensions

Surface area is the total area of the surface of a 3-dimensional object.

• The surface area of a prism or cylinder can be found using the formula: 2B + Lateral Area
  (Perimeter/circumference of base x length)
  In the contracted form, the SA of a cylinder would be: 2πrh + 2πr² and a rectangular prism would be: 2(wl+hl+hw)
  
  Practice with the Python Program below:
  
  "Do you want to practice finding the surface area of a cylinder or prism
  (type 'c' for cylinder and 'p' for prism):"


• The surface area of a pyramid can be found using the formula: B + Lateral Area (Perimeter x slant height/2)
  
  Practice with the Python Program below:
  
  "What's the surface area of a pyramid with length (6), width(3), and height (9)?"


• The surface area of a cone can be found using the formula: πr^2 +πrl)
  Practice with the Python Program below:
  
  "What's the surface area of a cone with radius (5), and slant height(10)? Use 3.14 for π and round to nearest tenth:"

Effects of Changing Dimensions

Modifying a shape’s dimensions can affect its perimeter, area, surface area and volume differently, depending on which dimension is adjusted.

Key Concepts:

1. Doubling, Tripling, Quadrupling, etc. a square's side length or a circle's radius will change its perimeter or circumference by the same factor of 2,3 and 4 respectively. i.e n[P(l)] = P(nl)
   Practice with the Python Program below:
   
   "Knowing that the perimeter of a square with side length 5 is 20, find the perimeter of another square whose side length is 13:"


2. Doubling, Tripling, Quadrupling, etc. a square's side length or a circle's radius will change its area by the squared factor of 4,9 and 16 respectively. i.e n^2[A(l)] = A(nl)
   Practice with the Python Program below:
   
   "Knowing that the area of a square with side length 3 is 9, find the perimeter of another square whose side length is 18:"


3. Doubling, Tripling, Quadrupling, etc. a cube's side length or a sphere's radius will change its volume by the cubed factor of 8,27 and 64 respectively. i.e n^3[V(l)] = V(nl)
   Practice with the Python Program below:
   
   "Knowing that the volume of a square with side length 4 is 64, find the perimeter of another square whose side length is 8:"