12.4 Volume of Cubes/Prisms/Cylinders

12.4 Volume of Cubes/Prisms/Cylinders

Volume

• The past couple of lessons, we have looked at Surface Area of different 3 dimensional shapes

• Surface Area was simply the measure of the total area that the shape occupies; like if we were painting it

• Volume is about what's on the inside of a 3-D shape; if you were to fill that shape with a liquid, how much liquid essentially.

Prisms

• Because these shapes are essentially an elongated base (look at the triangular prism...it's just a really long triangle!), we just take the area of the base, and times it by how long the 3-d shape is.

Volumes of Prisms

• Like always, start with finding the area of the base (it's a triangle)

• Next, we take that area of the base, and multiply by how long the shape is...so 12

•  $\frac{8\cdot3}{2}=12$  (base area)

•  $12\cdot12\left(length\right)=144cm^3$  

• *Notice the units is cubed...not squared anymore!

Fill in the Blank

Find the volume of this triangular prism (Have to find the height of the triangle!...Pythagorean theorem?) No units

Cylinders

• Similar to the prisms, we start with finding the base area (the base is a circle, so find the area of the circle)

• Take that area of the circle, and multiply by how tall the cylinder is (15 cm)

•  $3015.9cm^3$  = Volume of Cylinder

  
  

Fill in the Blank

Find the volume of this cylinder - Round to nearest tenth, no units

Show me your notes when you are finished