1. Standard: Determine the volume of prisms and pyramids (J).
Math 8C Unit 8 – Day 8
Standard:
Determine the volume of prisms and pyramids (J).

2. These measurements are always perpendicular to each other!
Recall!
Area
Area of a rectangle with length 𝑙 and width 𝑤
Area of a triangle with height ℎ and base 𝑏
Area of a circle with radius 𝑟
𝑹𝒆𝒎𝒆𝒎𝒃𝒆𝒓!
These measurements are always perpendicular to each other!
𝐴=𝑙∙𝑤
𝐴= 1 2 𝑏∙ℎ
𝐴=𝜋∙ 𝑟 2

3. Warm Up Determine the area of the figures below. 𝐴=2.25𝜋 𝑦 𝑑 2 ≈7.07
𝐴=42 𝑐 𝑚 2
𝐴=2.25𝜋 𝑦 𝑑 ≈7.07

4. 𝑽𝒐𝒍𝒖𝒎𝒆=𝒍𝒆𝒏𝒈𝒕𝒉 ∙𝒘𝒊𝒅𝒕𝒉∙𝒉𝒆𝒊𝒈𝒉𝒕
Warm Up
Determine the volume of the figures below.
𝑉=396 𝑐 𝑚 3
𝑉=16𝜋 𝑐 𝑚 3
𝑽𝒐𝒍𝒖𝒎𝒆=𝒍𝒆𝒏𝒈𝒕𝒉 ∙𝒘𝒊𝒅𝒕𝒉∙𝒉𝒆𝒊𝒈𝒉𝒕
𝑽𝒐𝒍𝒖𝒎𝒆=𝝅∙ 𝒓 𝟐 ∙𝒉𝒆𝒊𝒈𝒉𝒕

5. Prisms
A Prism is a solid, 3 dimensional figure whose two end faces are congruent polygons, and whose sides are parallelograms.
Example:

6. Volume of Prisms… Remember this?
𝑉=𝑙∙𝑤∙ℎ or 𝑉=(𝑎𝑟𝑒𝑎 𝑜𝑓 𝑏𝑎𝑠𝑒)∙ℎ
Example
Find the volume of each prism.
𝑉=60𝜋 𝑐 𝑚 3 ≈188.5 𝑐 𝑚 3
𝑉=10,716 𝑐 𝑚 3

7. Volume of Prisms 𝑉=𝑙∙𝑤∙ℎ Example 𝑉 𝑇 =843.75 𝑓𝑡 3 𝑉 𝐵 =15.625 𝑓𝑡 3
How many boxes will fit in the truck?
𝑉 𝑇 = 𝑓𝑡 3
𝑉 𝐵 = 𝑓𝑡 3
54 𝑏𝑜𝑥𝑒𝑠

8. Pyramids
A Pyramid is a solid, 3 dimensional figure whose base is a polygon, and whose sides are triangles who meet at an apex (the top point).
Example:

9. Pyramids
How many pyramids can you fit in a prism if you cut from vertex to vertex?
6 Pyramids!
Since the height of the prism is twice the height of each pyramid, we could pull a total of three pyramids out of the volume of the prism.
So the volume of one of these three pyramids is the volume of the prism.
Volume of a pyramid: 𝑉= 1 3 ∙𝑙∙𝑤∙ℎ or 𝑉= 𝑙∙𝑤∙ℎ 3

10. Pyramids Example: 𝑉=180 𝑚 3 𝑉=112 𝑖𝑛 3
Find the volume of the pyramids below
𝑉=180 𝑚 3
𝑉=112 𝑖𝑛 3

11. Pyramids
The Luxor Hotel in Las Vegas, Nevada has a base of 360,000 square feet and a height of 350 feet. What is its volume?
𝑉=42,000,000 𝑓𝑡 3

12. In Class Practice
U8D8 – ICP