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

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

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 2 ≈7.07

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

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

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

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 =843.75 𝑓𝑡 3 𝑉 𝐵 =15.625 𝑓𝑡 3 54 𝑏𝑜𝑥𝑒𝑠

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:

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 1 3 the volume of the prism. Volume of a pyramid: 𝑉= 1 3 ∙𝑙∙𝑤∙ℎ or 𝑉= 𝑙∙𝑤∙ℎ 3

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

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

In Class Practice U8D8 – ICP