how to find the area of a circle by guid765

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Guide teaches you how to find the area of a circle

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									                        Perimeter, Area and Volume Notes

Perimeter and circumference are the distance around a figure. The units for perimeter are the
same as the given units for a side or radius.

Area is the amount of space inside a 2-dimensional plane figure. The units for area are always
square units.

Given centimeters  area square centimeters
Given inches  area square inches
Square centimeters = sq cm = cm 2
Square inches = sq in = in 2

Volume is the amount of space inside a 3-dimensional figure. The units for volume are always
cubic units.

Given centimeters  volume cubic centimeters
Given inches  volume cubic inches
Cubic centimeters = cm 3
Cubic inches = in 3



FINDING PERIMETER

To find the perimeter of any polygon find the sum of the lengths of the sides.

Examples:

1.) Find the perimeter of the given triangle.




Solution: P = 18+26+28
          P = 72 centimeters

   Be sure to include the units (centimeters)
2. Find the perimeter of a hexagon given that each side has a length of 20 inches.

Solution: A hexagon has 6 sides. Add all sides together.

20 + 20 + 20 + 20 + 20 + 20 = 120 in or since all the sides are the same length 6(20) = 120 in



3. Find the perimeter of a square with sides of 6 miles.

Solution: Since the sides of a square are all equal, the perimeter is
6 + 6 + 6 + 6 = 24 miles or 4(6) = 24 miles



4. Find the perimeter of a rectangle with length 8 inches and width 5 inches.

Solution: Sketch the rectangle.




Since the opposite side of a rectangle are  , we know the lengths of the other sides of the
rectangle.




We can add all four sides: 8 + 5 + 8 + 5 = 26 inches or since the sides are  , 2*l + 2*w = 2(8) +
2(5) = 16+10 = 26 in.




The perimeter of a circle is called circumference.
C =  d or C=2  r.
Since you are not using a calculator we will leave the answer in terms of   .
Examples:

1. Find the circumference of a circle with a radius 12 inches.

Solution:            r = 12
                    C = 2 r
                    C = 2  (12)
                    C = 24  inches.



2. Find the circumference of a bike wheel whose diameter is 16 inches.

Solution:           C= d
                    C =  (16)
                    C = 16  inches.
Or
If the diameter is 16, the radius is 8 inches. (The radius is ½ of the diameter).

Now use the formula C = 2  r.
                    C = 2  (8)
                    C = 16  inches.



3. Find the circumference of a pool with radius 25 ft.

Solution:               C = 2 r
                        C = 2  (25)
                        C = 50  feet.



FINDING AREA

Examples:

1) Find the area of a triangle with height 8cm and base 12cm.

                                        1                  1
Solution:                      Area =     * base * height = * b * h
                                        2                  2
                                   1
                               A=    * 8 * 12
                                   2
                               A = 48 cm 2 or 48 square centimeters.
2) Find the area of a rectangle with length 15 cm and width 10cm.

Solution:                     Area = length * width = l * w.
                              A =15 * 10
                              A = 150 cm 2



3) Find the area of the given triangle.




Solution: In a right triangle, the base and height are the two perpendicular legs.

                                   1
                              A=     b*h
                                   2
                                   1
                                 = *6*8
                                   2
                                 = 3*8
                                 =24 in 2


4) Find the area of the parallelogram.




Solution: Area of a parallelogram = base * height

                              A = b*h
                                = 25 * 10
                                = 250 in 2
(The 12 is a side. The height and base are always    to each other.)
5) Find the area of a circle with a radius 6m.

Solution:              A =  r2
                       A =  (6) 2
                       A = 36  m 2


6) Find the area of a circle with diameter 20 in.

Solution: We need the radius for the area formula.

                              A=   r 2 , r = 10
                              A =  (10) 2
                              A =  (100)
                              A = 100  in 2




7) Find the area of the shaded region.




Solution: Find the area of the large rectangle minus the area of the small rectangle.




A L = 6*8                A s = 2*4                     A Shaded = 48-8
            2                      2
   = 48 m                   =8m                              = 40 m 2
8) Find the area of the shaded region.




Solution: Find the area of the large circle minus the area of the small circle.




AL =  r2                     As=     r2                  A Shaded = 36  - 16 
   =  62                        =  (4) 2                       = 20  cm 2
   =  * 36                      =  * 16
   = 36  cm 2                      = 16    cm 2




FINDING VOLUME

Examples:

1) Find the volume of a box with length 8in, width 10in, and height 10in.

Solution:       V=l*w*h
                 = 8 * 10 * 10
                 = 80 * 10
                 = 800 in 3
2) A fish tank is 20in long, 15in wide, and 15in high. How much water does the tank hold (one
gallon = 231 in 3 )?

Solution:       V = l*w*h
                 = 20 * 15 * 15
                 = 300 * 15 in 3
                  = 4,500in 3

                           1 gallon   x gallons
Use a proportion:                 3
                                    =
                            231in      4500in3

Cross multiply: 4500 * 1 = 231x
                  4500 = 231x
                     x  19.5




3) Find the volume of a cylinder with radius 4ft and height 5ft.

Solution: V=  r 2 h

            V     (4) 2 (5)
            V     *16*5
            V     *80
            V    80 ft 3




4) Find the volume of a can that is 6 inches tall and has a diameter of 10 inches.

Solution: V   r 2 h
          d =10 inches-----------------r = 5 inches

                  (5) (6)
                       2
            V
            V     *25*6
            V     *150
            V    150 in3
5) Find the volume of a ball with radius 3cm.

                                              4
Solution: Volume of a sphere =            V=     r3
                                              3
                                             4
                                          V =  (3)3
                                             3
                                                     4
                                               V =  *27
                                                     3
                                               Cross cancel
                                                      4      9
                                               V=        27
                                                     13
                                               V = 4 *9
                                               V = 36 cm3




6) Find the volume of a cube with length of a side 3ft.

Solution:     (edge = e)                           V = e3
                                                    V = 33 or 3 * 3 * 3
                                                    V = 27 ft 3
Practice Perimeter, Area and Volume


Directions: Find the perimeter, area or volume. Pay special attention to units.

1. Find the perimeter of a square with side 7in.

2. Find the area of a square with side 9in.

3. Find the area of




4. Find the area of




5. Find the area of a circle with diameter 14in.


6. Find the volume of a can with height of 9ft and diameter 10ft.


7. Find the volume of a ball with diameter10m.


8. Find how much fence is needed to go around a lot that is 1000 feet by 800 feet.


9. Find how much tile is needed to cover a room 30 by 60 .


10. A roll of aluminum foil is 12 inches wide and 75 feet long. Find the area of the roll of
aluminum.




                                       See answers below.
Answers to Practice.

1. P = 7*4 = 28 inches


2. A = 9 2 or 9 * 9 = 81 in 2


3. A = 9 * 4 = 36 in 2


         1
4. A =     * 20 * 8 = 10 *8 = 80 in 2
         2


5. d = 14, r = 7, A=  r 2   (7) 2   * 49  49 cm2 = 153.86 cm2


6. r = 5, V   r 2 h   (5) 2 (9)   * 25*9  225 ft 3 = 706.5 ft3


         4 3 4            4           4000
7. V =      r   (10)3   (1000)        m3 = 4,186.7 m3 (rounded to tenths place)
         3      3         3             3


8. P = 2l+2w=2(1000) + 2(800) = 2000 + 1600 = 3600ft or 1000 + 1000 + 800 + 800 = 3600ft


9. A = l * w = 30 * 60 = 1800sq ft.


10. ** Caution the units are different.
       Change 12in = 1ft
       A = l * w = 75 * 1 = 75 sq ft.

								
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