M8 L100 Surface Area of Pyramids & Cones

Surface Area of Pyramids & Cones

Math 8 Lesson 100

Lateral Surface Area of a Pyramid

The lateral surface area of a pyramid is the area of the surfaces above the base.

There are two ways to find the lateral surface area of a pyramid

The first way is to find the area of each triangular face and add them

Multiple Choice

Find the lateral surface area by adding the areas of each triangular face.

• 12

• 24

• 36

• 48

Multiple Choice

Find the lateral surface area by adding the areas of each triangular face.

• 12

• 24

• 36

• 48

Lateral Surface Area of a Pyramid

There are two ways to find the lateral surface area of a pyramid

The second way is to find the perimeter of the base (p) and slant height (s) and use this formula for Lateral Surface Area (As) 

 $A_s=\frac{ps}{2}$  

Multiple Choice

Find the lateral surface area by using the formula. $A_s=\frac{ps}{2}$  

• 12

• 24

• 36

• 48

Multiple Choice

Find the lateral surface area by using the formula. $A_s=\frac{ps}{2}$  

• 15

• 24

• 30

• 60

Total Surface Area of a Pyramid

To find the total surface area of a pyramid, add the lateral surface area to the area of the base

Total Surface Area = Lateral Area + Base Area

Multiple Choice

Find the total surface area by adding lateral area to base area. 

• 36

• 24

• 30

• 33

Multiple Choice

Find the total surface area.

• 24

• 36

• 48

• 64

Multiple Choice

Find the lateral surface area of this regular hexagonal pyramid.

• 240

• 360

• 432

• 864

Lateral Surface Area of a Cone

The lateral surface area of a cone is the area above the base.

To find the lateral surface area of a cone multiply radius (r), slant height (s) and pi ( $\pi$  )

Lateral Surface Area = 

 $A_s=\pi rs$  

Multiple Choice

Find the lateral surface area of a cone with slant height 10 and radius 2.

• $10\pi$

• $20\pi$
  

• $15\pi$
  

• $30\pi$
  

Multiple Choice

Find the lateral surface area of a cone with diameter 20 and height 24

•  $140\pi$ 

•  $180\pi$ 
  

•  $260\pi$ 
  

•  $260\pi$ 
  

Total Surface Area of a Cone

To find the total surface area of a cone add lateral surface area to the area of the base.

Total Surface Area = 

 $A_{ }=\pi rs\ +\ \pi r^2$  

Multiple Choice

Find the total surface area of a cone with diameter 20 and height 24

•  $240\pi$ 

•  $180\pi$ 
  

•  $260\pi$ 
  

•  $360\pi$ 
  

Multiple Choice

Find the lateral surface area of a cone with slant height 50 and height 48

•  $1400\pi$ 

•  $1596\pi$ 
  

•  $700\pi$ 
  

•  $896\pi$ 
  

Multiple Choice

Find the total surface area of a cone with slant height 50 and height 48

•  $1400\pi$ 

•  $1596\pi$ 
  

•  $700\pi$ 
  

•  $896\pi$ 
  

Multiple Choice

Find the lateral surface area of a pentagonal pyramid with 10 mm side length and slant height 16mm.

•  $400$ 

•  $156$ 
  

•  $700$ 
  

•  $800$ 
  

Multiple Choice

Find the total surface area of a pentagonal pyramid with 230 mm squared base area, 10 mm side length and slant height 16mm.

•  $400$ 

•  $156$ 
  

•  $700$ 
  

•  $630$ 
  

Multiple Choice

Find the total surface area of a hexagonal pyramid with 288 cm squared base area, 12 cm side length and slant height 22 cm.

•  $400$ 

•  $156$ 
  

•  $1080$ 
  

•  $630$