6th Grade Math Textbook, Fundamentals

Lesson 11-10 for exercise sets. &KDSWHU 

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Find the surface area and volume for each figure. Use 3.14 to approximate .

Round to the nearest tenth, if necessary.

1. 
   
   
   
   2. 
      
      
      
      3. 
         
      
      
      
      
   
   
   
   

4.Write and Discuss Why is the slant height of a pyramid always greater

than the height of the pyramid?

40 ft

15 ft

24 ft

10 ft

9 ft

8 ft

6 ft

5 ft

9 ft 7 ft

24 mm 96 mm 13 mm

5 mm

This figure was formed by placing half of a cylinder along

one lateral face of a triangular prism.

Find the volume of this figure. Use 3.14 to approximate .

Where necessary, round to the nearest 0.1 in.^3

Volume of triangular prism: VBh[ ( )( )] 32 15 in.^3

Volume of half of cylinder: V Bh (r^2 )h (()

2

)^32 r • 

(3.14) 33.2 in.^3

Volume of the figure: V 15 33.2 48.2 in.^3

So the volume of this figure is about 48.2 cubic inches.

169

16

13

16

13

8

1

2

13

16

1

2

1

2

1

2

3

2

5

8

1

2

1

About how many cubic inches of plastic will be used for each replica?

The souvenir is created by placing a square pyramid on top

of a rectangular prism. The height of the prism is given,

and the height of the complex figure is given. So you need

to subtract to find the height of the pyramid.

h 5  5  5  5  in.

Now find the volume of each figure.

Volume of the pyramid: V Bh ( • )  in.^3

Volume of the rectangular prism: VBh( • )  in.^3

Find the sum of the volumes to the nearest 0.1 in.^3

Volume of the Souvenir 

1.4 in.^3

So the manufacturer requires about 1.4 cubic inches of plastic for each souvenir.

Volume of

Pyramid

89

64

11

8

1

64

Volume of

Rectangular Prism

11

8

11

2

1

2

1

2

1

64

3

16

1

3

1

2

1

2

1

3

1

2

3

16

8

16

11

16

11

(^161)
5 in. 2
1
2 in.
3
16 in.  height
5
16 in.  slant height
13
8 in.
32 in.
3
2 in.
5
8 in.