1. Prisms

2. Page 1
Prisms
A prism has two parallel faces, called bases, that are congruent polygons.
The lateral faces are rectangles in a right prism, or parallelograms in an oblique prism.
Lateral faces

3. Volume of a Prism B = Area of the base h = the height of the prism
Page 1
Volume equals BIG B times h!
B = Area of the base
h = the height of the prism

4. Rectangular Prisms 𝑉=𝐵ℎ 𝑆𝑖𝑛𝑐𝑒 𝐵=𝑙𝑤 𝑉=(𝑙𝑤)ℎ 𝑉=(7)(5)(4) 𝑉=140 𝑉=𝑙𝑤ℎ
Page 2
A rectangular prism has rectangular bases and lateral edges perpendicular
to the bases.
Lets find the volume and surface
area of the prism shown!
𝑉=𝐵ℎ
𝑆𝑖𝑛𝑐𝑒 𝐵=𝑙𝑤
𝑉=(𝑙𝑤)ℎ
𝑉=(7)(5)(4)
𝑉=140
𝑉=𝑙𝑤ℎ
Useful Formula: Volume of a Rectangular Prism!

5. Examples
Page 3
𝐴𝐵𝐶𝐷≅𝐸𝐹𝐺𝐻
𝐴𝐵𝐹𝐸≅𝐶𝐺𝐻𝐷
𝐴𝐸𝐻𝐷≅𝐵𝐹𝐺𝐶

6. 𝑉=𝐵ℎ 𝐹𝑖𝑛𝑑 𝐵 𝑓𝑖𝑟𝑠𝑡, 𝑡ℎ𝑒𝑛 𝑠𝑢𝑏 𝑖𝑛 −𝑜𝑟− 𝑉=( 1 2 𝑙𝑤)ℎ 𝑉= 1 2 10 10 3 𝑉=150
Page 4
𝑉=𝐵ℎ
Since B = a triangle, use the area formula for a triangle.
𝑉=( 1 2 𝑙𝑤)ℎ 𝑉=
𝐹𝑖𝑛𝑑 𝐵 𝑓𝑖𝑟𝑠𝑡, 𝑡ℎ𝑒𝑛 𝑠𝑢𝑏 𝑖𝑛
𝑉=150
𝐵= 1 2 𝑏ℎ
𝑉=𝐵ℎ
−𝑜𝑟−
𝑉=(50)(3)
𝐵= 1 2 (10)(10)
𝑉=150
𝐵=50

7. 𝑉=𝐵ℎ 𝑉=𝑙𝑤ℎ 𝑡𝑟𝑖𝑝𝑙𝑒 𝑡ℎ𝑒 𝑙𝑒𝑛𝑔𝑡ℎ= 3𝑙 𝑡𝑟𝑖𝑝𝑙𝑒 𝑡ℎ𝑒 𝑤𝑖𝑑𝑡ℎ= 3𝑤
Page 4
𝑉=𝐵ℎ
Since B = a rectangle, use the area formula for a rectangle.
𝑉=𝑙𝑤ℎ
𝑡𝑟𝑖𝑝𝑙𝑒 𝑡ℎ𝑒 𝑙𝑒𝑛𝑔𝑡ℎ= 3𝑙
𝑡𝑟𝑖𝑝𝑙𝑒 𝑡ℎ𝑒 𝑤𝑖𝑑𝑡ℎ= 3𝑤
𝑡𝑟𝑖𝑝𝑙𝑒 𝑡ℎ𝑒 ℎ𝑒𝑖𝑔ℎ𝑡= 3ℎ
𝑁𝐸𝑊 𝑉𝑂𝐿𝑈𝑀𝐸:
𝑉=3𝑙∙3𝑤∙3ℎ
𝑉=27∙𝑙𝑤ℎ

8. Page 4
𝑉= 𝑒 3
𝑉= 8 3
𝑉=512

9. 𝑉𝑜𝑙𝑢𝑚𝑒 𝑆ℎ𝑜𝑒 𝐵𝑜𝑥 𝑉𝑜𝑙𝑢𝑚𝑒 𝑇𝑟𝑖. 𝑃𝑟𝑖𝑠𝑚 𝑉=𝐵ℎ 𝑉=48ℎ 𝑉= 48 6 288=48ℎ 𝑉=288
Page 4
𝑉𝑜𝑙𝑢𝑚𝑒 𝑆ℎ𝑜𝑒 𝐵𝑜𝑥
𝑉𝑜𝑙𝑢𝑚𝑒 𝑇𝑟𝑖. 𝑃𝑟𝑖𝑠𝑚
𝑉=𝐵ℎ
𝑉=48ℎ
𝑉= 48 6
288=48ℎ
𝑉=288
288=48ℎ
6=ℎ

10. 𝑉=𝐵ℎ 𝑉=( 1 2 𝑙𝑤)ℎ 48= 1 2 8 8 ℎ 48=32ℎ 1.5=ℎ Page 4
Since B = a triangle, use the area formula for a triangle.
𝑉=( 1 2 𝑙𝑤)ℎ
48= ℎ
48=32ℎ
1.5=ℎ

11. 𝑉=𝐵ℎ 𝑉=𝑙𝑤ℎ 𝑉= 𝑡+2 𝑡 3𝑡 𝑉= 𝑡+2 3 𝑡 2 𝑉=3 𝑡 3 +6 𝑡 2 Page 4
Since B = a rectangle, use the area formula for a rectangle.
𝑉=𝑙𝑤ℎ
𝑉= 𝑡+2 𝑡 3𝑡
𝑉= 𝑡+2 3 𝑡 2
𝑉=3 𝑡 3 +6 𝑡 2

12. Page 5

13. 𝑉=𝐵ℎ 𝑉=𝑙𝑤ℎ 𝑑𝑜𝑢𝑏𝑙𝑒 𝑡ℎ𝑒 𝑙𝑒𝑛𝑔𝑡ℎ= 2𝑙 𝑑𝑜𝑢𝑏𝑙𝑒 𝑡ℎ𝑒 𝑤𝑖𝑑𝑡ℎ= 2𝑤
Page 5
𝑉=𝐵ℎ
Since B = a rectangle, use the area formula for a rectangle.
𝑉=𝑙𝑤ℎ
𝑑𝑜𝑢𝑏𝑙𝑒 𝑡ℎ𝑒 𝑙𝑒𝑛𝑔𝑡ℎ= 2𝑙
𝑑𝑜𝑢𝑏𝑙𝑒 𝑡ℎ𝑒 𝑤𝑖𝑑𝑡ℎ= 2𝑤
𝑞𝑢𝑎𝑑𝑟𝑢𝑝𝑙𝑒 𝑡ℎ𝑒 ℎ𝑒𝑖𝑔ℎ𝑡= 4ℎ
𝑁𝑒𝑤 𝑉𝑜𝑙𝑢𝑚𝑒: 𝑉=2𝑙∙2𝑤∙4ℎ
𝑉=16𝑙𝑤ℎ

14. Page 5
𝑉=𝐵ℎ
Since B = a rectangle, use the area formula for a rectangle.
𝑉=𝑙𝑤ℎ 𝑉=
𝑉=72

15. Page 6
𝑉=𝐵ℎ
𝑉=𝑙𝑤ℎ 𝑉=
Since B = a rectangle, use the area formula for a rectangle.
𝑉=288

16. Page 6
𝑉= 𝑒 3
𝑉= 𝑒 3
8= 𝑒 3
216= 𝑒 3
3 8 = 3 𝑒 3
3 216 = 3 𝑒 3
2=𝑒
6=𝑒

17. Page 6
𝑉=𝐵ℎ
42=𝐵∙3
14=𝐵

18. Page 6
𝑉= 1 2 𝑑 1 ∙ 𝑑 2 ∙ℎ
𝑉=𝐵ℎ 𝑉=
Since B = a rhombus, use the area formula for a rhombus that utilizes the diagonals.
𝑉=1920
𝐵 𝑟ℎ𝑜𝑚𝑏𝑢𝑠 = 1 2 𝑑 1 ∙ 𝑑 2

19. Page 6
Since B = a rectangle, use the area formula for a rectangle.
𝑉=𝑙𝑤ℎ
51840= ℎ
8∙6480=51840
51840=1728ℎ 24
30=ℎ 72
𝑉=𝐵ℎ
Minimum height is 30 inches

20. Homework
Page 6
#2,4,5c,d,e,7,9,19

21. Page 6
𝑉= 𝑒 3
𝑉= 25 3
𝑉=15625

22. Page 6
𝑉=𝐵ℎ
𝑉= 𝑠 2 ℎ
𝑉= 7 2 ∙3
Since B = a square, use the area formula for a square.
𝑉=147

23. Page 6
𝑉= 𝑒 3
𝑉= 𝑒 3
𝑉= 𝑒 3
64= 𝑒 3
125= 𝑒 3
27= 𝑒 3
3 64 = 3 𝑒 3
3 125 = 3 𝑒 3
3 27 = 3 𝑒 3
4=𝑒
5=𝑒
3=𝑒

24. Page 6
𝑉=𝐵ℎ
9=18ℎ
9 18 = ℎ
1 2 =ℎ

25. 𝑉=𝐵ℎ 𝑉= 1 2 𝑑 1 ∙ 𝑑 2 ∙ℎ 60= 1 2 10∙12 ℎ 60=60ℎ 1=ℎ Page 6
𝑉= 1 2 𝑑 1 ∙ 𝑑 2 ∙ℎ
𝑉=𝐵ℎ
60= ∙12 ℎ
Since B = a rhombus, use the area formula for a rhombus that utilizes the diagonals.
60=60ℎ
1=ℎ

26. Page 6
𝑉=𝐵ℎ
𝑉=10𝐵ℎ
The volume would be 10 times the original volume.