1. Unit 2: Engineering Design Process
Foundations of Technology
Unit 2: Engineering Design Process
Lesson 5: Prototyping and Modeling
3 Calculating Area and Volume

2. The Big Idea
Big Idea:
At various intervals of the Engineering Design Process, conceptual, mathematical and physical models are used to evaluate the design solution.

3. Area and Volume Definitions:
Area – the amount of space inside a two- dimensional shape.
Surface area – the total area of all surfaces on a three-dimensional object.
Volume – the amount of space a three- dimensional object occupies.

4. Area Square: a = the length of all sides, as all sides are equal
Equation for Area (A) =
s X s = s² = A s s s s

5. Area Rectangle: W = the width of rectangle H = the height of rectangle
Equation for Area (A) = W x H = A W H

6. Area Triangle: b = the base of the triangle
h = the height of the triangle
Equation for Area (A) = ½(b x h) = A h b

7. Area Circle: r = the radius of the circle
Equation for Area (A) = π(r²) = A r

8. Practice Questions Calculate the area for the square and rectangle:
W = 3
H = 2

9. Practice Questions Calculate the area for the square and rectangle
W = 3
Area = a² = 4²
A = 16
Area = W x H = 3 x 2
A = 6
H = 2

10. Practice Questions Calculate the area for the triangle and circle:
b = 4

11. Practice Questions Calculate the area for the triangle and circle:
Area = π(r²) = π(2.5²)
= π(6.25)
A = 19.6
Area = ½(b x h) = ½(4 x 3)
= ½(12)
A = 6
b = 4

12. Surface Area
Cube:
a = the length of all sides, as all six sides are equal
Equation Surface Area (SA) = 6(s²) = SA s s s

13. Surface Area Rectangular Prism: W = the width of the prism
D = the depth of the prism
H = the height of the prism
Equation Surface Area (SA) = 2(W x H) + 2(D x H) + 2(W x D) = SA W D H

14. Surface Area Sphere: r = the radius of the sphere
Equation Surface Area (SA) = 4π(r²) = SA r

15. Surface Area Cylinder: r = the radius of the cylinder
h = the height of the cylinder
Equation Surface Area (SA) = 2π(r²) + 2π(r x h) = SA h r

16. Practice Question
Calculate the surface area for the sphere and cylinder:
H = 3
s = 2
D = 2
W = 4

17. Practice Question
Calculate the surface area for the cube and rectangular prism:
H = 3
s = 2
D = 2
W = 4
Surface Area = 2(W x D) + 2(H x D) + 2(W x H)
= 2(4 x 2) + 2(3 x 2) + 2(4 x 3)
= 2(8) + 2(6) + 2(12) =
SA = 52
Surface Area = 6s²
= 6(2²)
= 6(4)
SA = 24

18. Practice Question
Calculate the surface area for the sphere and cylinder:
r = 2
h = 6
r = 1

19. Practice Question
Calculate the surface area for the sphere and cylinder:
Surface Area = 2π(r²) + 2π(r x h) = 2π(1²) + 2π(1 x 6)
= 2π(1) + 2π(6)
= SA = 44
r = 2
h = 6
Surface Area = 4π(r²)
= 4π(2²)
= 4π(4)
SA = 50.24
r = 1

20. Volume of Cube and Prism
Volume of a Cube
V = s3
Volume of a
Rectangular prism
V = W x H x D s W D H

21. Volume of Sphere and Cylinder
Volume of a Sphere
V = 4/3∏(r³)
Volume of a Cylinder
(V) = ∏(r²)h r h r

22. Practice Question
Calculate the volume of the cube and rectangular prism:
H = 3
b = 2
D = 2
W = 4

23. Practice Question
Calculate the volume of the cube and rectangular prism:
H = 3
s = 2
D = 2
W = 4
Volume = W x D x H
V = 4 x 2 x 3
V = 24
Volume = s3
V = (23)
V = 8

24. Practice Question Calculate the volume of the sphere and cylinder:

25. Practice Question Calculate the volume of the sphere and cylinder:
Volume = ∏(r²)h
V = (3.14) (1.52) (6)
V = (3.14) (2.25) (6)
V = 42.39
r = 2
h = 6
Volume = 4/3∏(r³)
V = (1.33) (3.14) (23)
V = 4.19 x 8
V = 33.49
r = 1.5