Area and Volume

The area of a plane figure is the number of square units contained in the figure. The volume of a space figure is the number of cubic units contained in the figure. Formulas for area and volume are listed on page 693.

Example 1

Find the area of each figure.

1. 

   A = π r 2   ≈ 22 7 ⋅ ( 21 10 ) 2   = 693 50 = 13 43 50  in . 2 table with 3 rows and 2 columns , row1 column 1 , eh , column 2 equals pi , r squared , row2 column 1 , , column 2 almost equal to , 22 over 7 , dot . open , 21 over 10 , close squared , row3 column 1 , , column 2 equals , 693 over 50 , equals 13 , and 43 over 50 , in , . squared , end table

2. 

   A = 1 2 ( b 1 + b 2 ) h   = 1 2 ( 19 + 23 ) ⋅ 8.5   = 178.5  mm 2 table with 3 rows and 2 columns , row1 column 1 , eh , column 2 equals , 1 half . open . b sub 1 , plus , b sub 2 . close . h , row2 column 1 , , column 2 equals , 1 half . open , 19 plus 23 , close . dot 8.5 , row3 column 1 , , column 2 equals , 178.5 . mm squared , end table

Example 2

Find the volume of each figure.

1. 

   V = 4 3 π r 3   ≈ 4 3 ⋅ 3.14 ⋅ 2.7 3   = 82.40616 ≈ 82.4 m 2 table with 3 rows and 2 columns , row1 column 1 , v , column 2 equals , 4 thirds , pi , r cubed , row2 column 1 , , column 2 almost equal to , 4 thirds , dot , 3.14 , dot , 2.7 cubed , row3 column 1 , , column 2 equals , 82.40616 , almost equal to , 82.4 , m squared , end table

2. 

   V = 1 3 B h   = 1 3 ( 37 2 ) ⋅ 24   = 10 , 952  ft 3 table with 3 rows and 2 columns , row1 column 1 , v , column 2 equals , 1 third b h , row2 column 1 , , column 2 equals , 1 third . open , 37 squared , close . dot 24 , row3 column 1 , , column 2 equals 10 comma 952 , ft cubed , end table

Exercises

Find the exact area of each figure.

Find the exact volume of each figure.

5. 
6. 
7. 
8. 
9. Find the area of a triangle with a base of 17 in. and a height of 13 in.
10. Find the volume of a rectangular box 64 cm long, 48 cm wide, and 58 cm high.
11. Find the surface area of the cube in Exercise 5.

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