8-3 Intro to Pyramids and Cones

Intro to Pyramids and Cones

Geometry LEE 2020-21

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Multiple Choice

How would you describe the base of this pyramid?

• Triangle with sides 15, 16, 17

• Isosceles triangle with altitude 17 and base 16

• Square with sides 16

• Parallelogram with sides 16 and 17

Multiple Choice

What is the perimeter of the base of this square pyramid?

• 16

• 60

• 64

• 68

Perimeter of a Regular Figure

 $P=ns=4\left(16\right)=64$  

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Area of a Square

 $B=s^2=16^2=256$  

Multiple Choice

What is the lateral area of this pyramid?

 $LA=\frac{1}{2}pl$  

• 480

• 544

• 1024

• 1088

Lateral Area

 $LA=\frac{1}{2}pl=\frac{1}{2}\left(64\right)\left(17\right)=544$  

Fill in the Blanks

Total Area

 $SA=LA+B=544+256=800$  

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Multiple Choice

What is the slant height, $l$ , of the right cone shown here? 

• 2.4 cm

• 10.9 cm

• 13 cm

• 17 cm

Use Pythagorean triples to find missing sides

• 3, 4, 5

• 5, 12, 13 (this one answered previous question)

• 7, 24, 25

• 8, 15, 17

Multiple Choice

What is the radius, $r$ , of the right cone shown here? 

• 2 cm

• 8 cm

• 16 cm

• 32 cm

Pythagorean Triple 8,15,17

The height is 15, the slant height is 17. The missing value is 8.

Multiple Choice

What is the lateral area of the right cone? $LA=\pi rl$  

•  $60\pi\ cm^2$  

•  $65\pi\ cm^2$  

•  $156\pi\ cm^2$  

Lateral Area

 $LA=\pi rl=\pi\left(5\right)\left(13\right)=65\pi$  

Multiple Choice

What is the area of the base of the right cone? $B=\pi r^2$  

•  $25\pi\ cm^2$  

•  $144\pi\ cm^2$  

•  $169\pi\ cm^2$  

Base (Area of Circle)

 $B=\pi r^2=\pi\left(5\right)^2=25\pi$  

Multiple Choice

What is the total surface area the right cone? $SA=LA+B=\pi rl+\pi r^2$  

•  $85\pi\ cm^2$  

•  $90\pi\ cm^2$  

•  $282.7\pi\ cm^2$  

Surface Area

 $SA=LA+B=65\pi+25\pi=90\pi$  
Note:  $90\times\pi\approx282.7$  but  $90\times\pi\ne282.7\pi$  

Poll

Compare cones to pyramids. For which solid do you think is easier to calculate the surface area?

• Pyramids

• Cones

• They are about the same