Geometry Unit 2 Review Day 1

Geometry Unit 2 Review Day 1

Ya'll ready for this?

Volume is

The amount of space inside a 3-D figure. OR

The number of unit cubes that fills a 3-D figure.

Prisms

Your test will have rectangular and triangular prisms.

You will have to find their:

Surface Area in units²

Volume in units³

Use the formulas!

Multiple Choice

How can you find the volume of this rectangular prism?

• Use the formula! V=lwh so multiply the length times the width times the height

• The other answer is the right one, click it!

Multiple Choice

Ok, now do it! Find the volume of this rectangular prism.

• 8

• 8 units³

• 18 units²

• 18 units³

OR think of B*h

Watch this vid to see why the area of the base (B) times the height is the same as length times width times height.

That explains the formula for volume of triangular prisms! (watch this 2 min video)

 $V=Bh$  
 $V=\left(b\times h\div2\right)h$  

Multiple Choice

Your turn. What is the base of this prism?

• The bottom! It's a rectangle.

• The triangles! The bases of a prism are parallel like the triangles. It doesn't matter that they aren't on the bottom.

Multiple Choice

Ok, so the bases are triangles. If

 $V=Bh$   and the bases are triangles, how do you find the area of a triangle?

•  $A=lw$  so multiply length times width

•  $A=bh$   so multiply the base of the red triangle by its height

•  $A=b\times h\div2$  so multiply the base of the red triangle by its hieght then divide by 2.

Multiple Choice

Ok! Get your calculator and do it. Find the volume of this triangular prism.

 $V=Bh$  or  $V=\left(b\times h\div2\right)h\$  

•  $\left(6\times4\div2\right)9=108\ ft^2$  

•  $\left(6\times5\div2\right)9=135ft^2$  

• I'm not sure about this one...

Multiple Choice

Find the volume of this triangular prism:

• 90

• 90 cm³

• 180

• 180 cm²

Multiple Choice

Find the volume of this rectangular prism. Do you remember the formula?

•  $V=lwh$  so V=16 cubic units

•  $V=\left(lw\div2\right)h$  so V=8 cubic units

•  $V=Bh$  so V=16 square units

Multiple Choice

Sometimes they give you the diameter of the circle. You have to cut it in half to get the radius before you can get your  $\pi r^2$  on. Try it!

•  $A=\pi\times12^2$  

•  $A=\pi\times6^2$  

•  $A=\pi\times6$  

Watch this video on Volume of a Cylinder:  $V=\pi r^2h$  

 $\pi\times r^2$  times the height

The base of the cylinder is the circle, so this is still V=Bh (area of the base times the height).

Poll

So volume of a cylinder is area of the circular base times the height. How are you at finding the area of a circle?

• I'm great at it!

• I think I've done that before...

• Say what now?

Multiple Choice

What is

 $\pi$  ? What is $r^2$  ?

•  $\pi$  is approximately 3.14 and r $r^2$   means radius to the second power (r x r).

Multiple Choice

 $A=\pi r^2$  

Ok, so now use the formula to find the area of this circle.

• Well, the radius is 7, so  $A=3.14\times7^2$  or 153.86 square units

• Well, the radius is 7, so  $A=3.14\times7^2$  or 43.96  square units

• Well, if the radius is 7 so the diameter is 14 and  $A=3.14\times14$  or 43.96

Poll

What's a diameter? Choose as many of these as you want.

• A diameter is a line that goes from one side of a circle to the other through the center.

• A diameter is two radii that make a straight line across the center of a circle.

• A diameter cuts a circle into two equal sized pieces.

• $2r=d$

• $r=\frac{1}{2}d$

Ok! We're ready now.

Volume of a Cylinder is Bh. That's

 $\pi r^2h$  

Multiple Choice

Find the volume of a cylinder with radius 5 inches and height 12 inches.

• 376.8 in³

• 78.5 in³

• 942 in³

• 60 in³

Multiple Choice

Find the volume of the cylinder.

• 21,600 mm³

• 16,956 mm³

• 720 mm³

Poll

How are you doing?

• Good! I think I'm getting it.

• Good! I fell asleep around slide 15 but now I'm back and well rested.

• AFK

• Geometry rocks!

• I need a break.

Let's take a break

Click play. I highly recommend dancing. No one will see you and it will get the blood flowing back up to your brain.

Volume of Pyramids and Cones

Prisms - have two parallel bases. Prisms - name starts with the parallel, congruent bases.

Pyramids -have one base.

Pyramids - name starts with the one base.

Watch this video. For volume, use these formulas:

•  $V=Bh\div3$  where B is the area of the base.

• rectangular pyramid:  $lwh\div3$  

• cone:  $\pi r^2h\div3$  

• Watch the video! It's short.

Multiple Choice

Find the volume of this prism.

•  $A=\left(10\times8\right)6\div3$  

• Pick the other one, it's right. It has the area of the base (10x8) times the height (6) divided by 3. That's the formula.

Multiple Choice

Find the volume of this cone.

• 32 in

• $V=\pi4^2\left(8\right)\div3$ 401.92 or about 4.2 square inches

• $V=\pi4^2\left(8\right)\div3$ 133.97 or about 134 square inches

• $V=\pi4^2\left(8\right)\div3$ or 32 square inches

Multiple Choice

Find the volume of this sphere. Spheres use this formula:

 $\frac{4}{3}\pi r^3$  
Fractions give you the heebie geebies? Try this:  $1.3333\pi r^3$  

•  $1.3333\times3.14\times8^{3^{ }}=1.3333\times3.14\times8\times8\times8$  

• 267.93 or about 268 cubic meters

• um... Can you show me one of these?

Sphere Volume

Don't forget to cube the radius, meaning r x r x r

This sphere has a radius=7

In the fourth step, you can use 1.3333 instead of 4/3.