Geometry Review - Unit 7

Geometry Review - Unit 7

Have your reference sheet ready!

Volume of 3-D Figures

• The measure of the amount of space occupied by a 3-D solid object

• Measured in cubic units

•  $B:$  area of the base

•  $h$  :  height

•  $r$  :  radius

•  $\pi$  ( $\sim$  3.14)

Multiple Choice

What is the formula used to find the volume of a prism?

• $V\ =\ Bh$

• $V\ =\ \frac{1}{2}Bh$

•  $V\ =\ Ph$  

•  $V=Ph+2B$  
  

Multiple Choice

Number of Edges?

• 3

• 4

• 5

• 6

Multiple Choice

Number of Vertices?

• 3
• 4
• 5
• 6

Multiple Choice

Number of Faces?

• 7
• 5
• 4
• 15

Multiple Choice

Which expression represents how to calculate the volume?

• 
   $V=\frac{1}{3}\pi\left(2\right)^2\cdot3$  

  
  

•  $V=\pi\left(2\right)^2\cdot3$  
  

•  $V=\frac{1}{3}\pi\left(3\right)^2\cdot2$  
  

•  $V=\frac{4}{3}\pi\left(2\right)^3$  
  

Multiple Choice

Find the volume using $3.14$  for  $\pi$  .  Round answer to the nearest hundredth.

•  ^{$5572\ cm^3$}  

•  ^{$506.59\ cm^3$}  

•  ^{$126.65\ cm^3$}  

•  ^{$1393.11\ cm^3$}  

Multiple Choice

 $V=Bh$  What does the "B" in the volume formula represent?

• Bottom of the object

• Base

• Bottom

• Area of the base

Multiple Choice

Find the volume using  $3.14$  for  $\pi.$ Round answer to the nearest tenth. 

•   $282.6\ in^3$  

•  $94.2\ in^3$  

•  $235.5\ in^3$  

•  $78.5\ in^3$  

Multiple Choice

Which expression represents how to calculate the volume?

•  $V=\pi\left(5\right)^2\cdot13$  
  

•  $V=\pi\left(5\right)^2\cdot12$  
  

•  $V=\frac{1}{3}\pi\left(5\right)^2\cdot12$  
  

•  $V=\pi\left(5\right)^3\cdot12$  
  

Multiple Choice

Which expression represents how to calculate the volume of the pyramid?

•  $V=10\cdot15\cdot12$  

•  $V=\frac{1}{3}\cdot10\cdot15\cdot12$  

•  $V=\frac{4}{3}\cdot10\cdot15\cdot12$  
  

•  $V=50\cdot12$  
  

Multiple Choice

An oblique prism has a volume of  $144\ units^3$  .  The area of the base is 25 square units.  What is the perpendicular height of the prism?  Round to the nearest whole number.

• 2 units

• 4 units

• 6 units

• 8 units

Poll

How do you feel about the problems we just solved? (3 being the most confident)

• 1

• 2

• 3

Similar solids:

• Same Shape

• Proportional Corresponding Measures

• Ratio of side lengths is

   $\frac{1}{2}$  or  $1:2$  

• SA will change by factor of  $\left(SF\right)^2$  

• Volume will change by factor of  $\left(SF\right)^3$  

Multiple Choice

If all of the dimensions of a triangular prism decreased by 1/3, how much would the volume decrease by?

• $\frac{1}{27}$

• $\frac{1}{9}$

• $\frac{1}{3}$
  

• $\frac{1}{6}$
  

Multiple Choice

Two similar pyramids have heights of 4 inches and 7 inches. What is the ratio of the volume of the small pyramid to the volume of the large pyramid?

• $4:7$

• $16:49$
  

• $64:343$
  

• $12:21$

Surface Area

• Total Surface Area: cumulative area of ALL the surfaces of a solid

• Lateral Face: in a prism or pyramid, any face that is not a base

• Lateral Area: in a prism or pyramid, the sum of the areas of the lateral faces; in a cylinder or cone, the area of the curved surface

•  $P:$  perimeter of the base

•  $l:$  slant height (height of lateral face)

•  $B:$  area of base

•  $h:$  height

Hexagonal Prism

• Bases are hexagons

• Lateral faces are rectangles

Cylinder

• Unique prism with circular bases

• Lateral SA:

   $2\pi rh$  

• Total SA:   $2\pi rh+2\pi r^2$  

Pyramid

• Lateral SA:

   $\frac{1}{2}Pl$  

• Total SA:   $\frac{1}{2}Pl+B$  

• Base is a polygon

• Lateral faces are triangles that converge at the apex.

• Named using the shape of the base

Multiple Choice

Describe the cross section.

• rectangle
• trapezoid
• parallelogram
• triangle

Multiple Choice

Describe the cross section.

• rectangle
• square
• parallelogram
• circle

Multiple Choice

Describe the cross section.

• trapezoid
• triangle
• rectangle
• square

Multiple Choice

Which expression represents how to calculate the total surface area?

•  $S=\left(54\right)\left(4\right)+2\left(10\cdot17\right)$  

•  $S=54\cdot14$  
  

•  $S=\left(54\right)\left(10\right)+2\left(4\cdot10\right)$  
  

•  $S=\left(170\right)\left(4\right)$  
  

Multiple Choice

A paper party hat, like the one shown, has a slant height of 6 inches and a height of 5 inches. How many square feet of cardboard would be needed to create this hat?

• 62.5 in.²
• 10 in.²
• 50 in.²
• 22.5 in.²

Multiple Choice

Find the surface area of the cone. Leave your answer in terms of pi.

• 12π m²

• 16π m²

• 24π m²

• 8π m²

Open Ended

Rate yourself on a scale of 1 to 3 and list 5 things that you learned today that will help you on your test.