Utility Of The Table. Examples

1. Required the circumference of a circle, the diameter being five inches ?

In the column of circumferences opposite the given diameter, stands 15.708* inches, the circumference required.

2. Required the capacity, in gallons, of a can the diameter being 6 feet and depth 10 feet ?

In the fourth column from the given diameter stands 211.4472* being the content of a can 6 feet in diameter and 1 foot in depth, which being multipled by 10 gives the required content, two thousand one hundred fourteen and a half gallons.

3, Any of the areas in feet multiplied by .03704, the product equal the number of cubic yards at 1 foot in depth.

4. The area of a circle in inches multiplied by the length or thickness in inches, and by .263, the product equal the weight in pounds of cast iron.

* See opposite page (page 40) for Decimal Equivalents to the Fractional parts of a Gallon, and an Inch.

Diameters And Circumferences Of Circles, And The Content In Gallons At 1 Foot In Depth

[Area in Inches.]

Diam.

Circ. in.

Area. in.

Gallons.

1 in.

3.1416

.7854

.04084

1/8

3.5343

.9940

.05169

¼4

3 9270

1.2271

.06380

3/8

4.3197

1.4848

.07717

½

4.7124

1.7671

.09188

5/8

5.1051

2.0739

.10784

¾

5.4978

2.4052

.12506

7/8

5.8.905

2.7611

.14357

2 in.

6.2832

3.1416

.16333

1/8

6.6759

3.5465

.18439

¼

7.0686

3.9760

.20675

3/8

7.4613

4.4302

.23036

½

7.8540

4.9087

.25522

5/8

8.2467

5.4119

.28142

¾

8.6394

5.9395

.30883

7/8

9.0321

6.4918

.33753

3 in.

9.4248

7.0686

.36754

1/8

9.8175

7.6699

.39879

¼

10.210

8.2957

.43134

3/8

10.602

8.9462

.46519

½

10.995

9.6211

.50029

5/8

11.388

10.320

.53664

¾

11.781

11.044

.57429

7/8

12.173

11.793

.61324

4 in.

12.566

12.566

.65343

1/8

12.959

13.364

.69493

¼

13.351

14.186

.73767

3/8

13.744

15.033

.78172

½

14.137

15.904

.82701

5/8

11.529

16.800

.87360

¾

14.922

17.720

.92144

7/8

15.315

18.665

.97058

5 in.

15.708

19.635

1.02102

1/8

16.100

20.629

1.07271

¼

16.493

21.647

1.12564

3/8

16.886

22.690

1.17988

½

17.278

23.758

1.23542

5/8

17.671

24.850

1.29220

¾

18.064

25.967

1.35028

7/8

18.457

27.108

1.40962

6 in.

18.849

28.274

1.47025

1/8

19.242

29.464

1.53213

¼

19.636

30.679

1.69531

3/8

20.027

31.919

1.65979

Diam.

Circ. in.

Area. in.

Gallons.

6½

20.420

33.183

1.72552

5/8

20.813

34.471

1.79249

¾

21.205

35.7S4

1.86077

7/8

21.598

37122

1.93934

7 in.

21.991

38.484

200117

1/8

22.383

39.871

2.07329

¼

22.776

41.282

214666

3/8

23169

42.718

222134

½

23.562

44.178

2.29726

5/8

23.954

45.663

2.37448

¾

24.347

47.173

2.45299

7/8

24.740

48.707

2 53276

8 in.

25132

50.265

2.61378

1/8

25515

51.848

2.69609

¼

25.918

53.456

2.77971

3/8

26.310

55.088

2.86458

½

26.703

56.715

2.95074

5/8

27.096

58 426

3.03815

¾

27.489

60132

3.12686

7/8

27.881

61.862

3.21682

9 in.

28.274

63 617

3.30808

1/8

28.667

65.396

3.40059

¼

29.059

67.200

3.49440

3/8

29.152

69.029

3.58951

½

29.845

70.882

3.68586

5/8

30.237

72.759

3.78347

¾

30 630

74.662

3.882 42

7/8

31.023

76.588

3.98258

10 in

31.416

78.540

4.08408

1/8

31.808

80.515

4.18678

¼

32.201

82.516

4.29083

3/8

32.594

84.540

4.39608

½

32.986

86.590

4.50268

5/8

33.379

88.664

4.61058

¾

33.772

90.762

4.71962

7/8

34.164

92.885

4.82846

11 in.

34 557

95.083

4.94172

1/8

34.950

97.205

5.05466

¼

35 343

99.402

5.16890

3/8

35.735

101.623

5.28489

½

36.128

103 869

5.40119

5/8

36.521

106.139

5.51928

¾

36.913

108.484

5.63857

7/8

37.806

110.753

5.75916

Diameters And Circumferences Of Circles

Diameters And Circumferences Of Circles, And The Content In Gallons At 1 Foot In Depth

[Area in Feet."]

Diam.

Circ.

Area in ft.

Gallons.

Ft

In.

Ft.

In.

1 ft. in depth

1

3

1 5/8

.7854

5.8735

1

1

3

4 5/8

.9217

6.8928

1

2

3

8

1.0690

7.9944

1

3

3

11

1.2271

9.1766

1

4

4

2 1/8

1.3962

10.4413

1

5

4

5 3/8

1.5761

11.7866

1

6

4

8½

1.7671

13.2150

1

7

4

11 5/8

1.9689

14.7241

1

8

5

2¾

2.1816

16.3148

1

9

5

5 7/8

2.4052

17.9870

1

10

5

9

2.6398

19.7414

1

11

6

2¼

2.8852

21.4830

2

6

3 3/8

3 1416

23.4940

2

1

6

6½

3.4087

25.4916

2

2

6

9 5/8

3.6869

27.5720

2

3

7

0¾

3.9760

29.7340

2

4

7

3 7/8

4.2760

32.6976

2

5

7

7

4.5869

34.3027

2

6

7

10¼

4.9087

36.7092

2

7

8

1 3/8

5.2413

39.1964

2

8

8

4½

5.5850

41.7668

2

9

8

7 5/8

5.9395

44.4179

2

10

8

10¾

6.3049

47.1505

2

11

9

1 7/8

6.6813

49.9654

3

9

5

7.0686

52.8618

3

1

9

8¼

7.4666

55.8382

3

2

9

l1 3/8

7 8757

58.8976

3

3

10

2½

8.2957

62 0386

3

4

10

5 5/8

8.7265

65.2602

3

5

10

8¾

9.1683

68 5193

3

6

10

11 7/8

9.6211

73.1504

3

7

11

3

10.0846

75.4166

3

8

11

6 1/8

10.5591

78.9652

3

9

11

9 3/8

11.0446

82.5959

3

10

12

5½

11.5409

86.3074

3

11

12

3 5/8

12.0481

90.1004

4

12

6¾

12.5664

93 9754

4

1

12

9 7/8

13.0952

97.9310

4

2

13

1

13.6353

101.9701

4

3

13

4 1/8

14.1862

103.0300

4

4

13

7¼

14.7479

110 2907

4

5

13

10i

15.3206

114.5735

Diam.

Circ.

Area in ft.

Gallons.

Ft.

In.

Ft.

In.

1 ft. in depth

4

6

14

1 5/8

15.9043

118.9386

4

7

14

4 5/8

16.4986

123.3830

4

8

14

7 7/8

17.1041

127.9112

4

9

14

11

17.7205

132.5209

4

10

15

2 1/8

18.3476

137.2105

4

11

15

5¼

18.9858

142.0582

5

15

8½

19.6350

146.8384

5

1

15

11 5/8

20.2947

151.7718

5

2

16

2¾

20.9656

156.7891

5

3

16

5¾

21.6475

161.8886

5

4

16

9

22.3400

167.0674

5

5

17

0 1/8

23.0437

172.3300

5

6

17

3¼

23.7583

177.6740

5

7

17

6 3/8

24.4835

183.0973

5

8

17

9 5/8

25.2199

188.6045

5

9

18

0¾

25.9672

194.1930

5

10

18

3 7/8

26.7251

199.8610

5

11

18

7 1/8

27.4943

205.6133

6

18

10 1/8

28.2744

211.4472

6

3

19

7½

30.6796

229.4342

6

6

20

4 7/8

33.1831

248.1564

6

9

21

4

35.7847

267.6122

7

21

11 7/8

38.4846

287.8032

7

3

22

9¼

41.2825

308.7270

7

6

23

6¾

44.1787

330.3859

7

9

24

4 1/8

47.1730

352.7665

8

25

1½

50.2656

375.9062

8

3

25

11

53.4562

399.7668

8

6

26

8 3/8

56.7451

424.3625

8

9

27

5¾

60.1321

449.2118

9

28

3¼

63.6174

475.7563

9

3

29

0 5/8

67.2007

502.5536

9

6

29

10 1/8

70.8823

530.0861

9

9

30

7½

74.6620

558.3522

10

31

5

78.5400

587 3534

10

3

32

2 3/8

82.5160

617.0876

10

6

32

11¾

86.5903

647.5568

10

9

33

9¼

90.7627

678.2797

Diameters And Circumferences Of Circles

Diam.

Circ.

Area in ft.

Gallons.

Ft.

In.

Ft.

In.

1 ft. in depth

11

34

6 5/8

95.0334

710.6977

11

3

35

4 1/8

99.4021

743.3686

11

6

36

1½

103.8691

776.7746

11

9

36

10 7/8

108.4342

8109143

12

37

8 3/8

113.0976

848.1890

12

3

38

5¾

117.8590

881.3966

12

6

39

3¼

1227187

917.7395

12

9

40

0 5/8

127.6765

954.8159

13

40

10

132.7326

992.6274

13

3

41

7½

137.8867

1031.1719

13

6

42

4 7/8

143.1391

1070.4514

13

9

43

2¼

148.4896

1108.0645

14

43

11¾

153.9384

1151.2129

14

3

44

9 1/8

159.4852

1192.6940

14

6

45

6 5/8

165.1303

1234.9104

14

9

46

4

170.8735

1277.8615

15

47

1½

176.7150

1321.5454

15

3

47

10 7/8

182.6545

1365.9634

15

6

48

8¼

188.6923

1407.5165

15

9

49

5¾

194.8282

1457.0032

16

50

3 1/8

201.0624

1503.6250

16

3

51

0½

207.3946

1550.9797

16

6

51

10

213.8201

1599.0696

16

9

52

7 3/8

220.3537

1647.8930

17

53

4 7/8

226.9806

1697.4516

17

3

54

2 1/8

233.7055

1747.7431

17

6

54

11 5/8

240.5287

1798.7698

17

9

55

4

247.4500

1850.5301

18

56

6½

254.4696

1903.0254

18

3

57

4

261.5872

1956.2537

18

6

58

1 3/8

268.8031

2010.2171

18

9

58

10¾

276.1171

2064.9140

19

59

8¼

288.5294

2120.3462

19

3

60

5 5/8

291.0397

2176.5113

19

6

61

3 1/8

298.6483

2233.2914

19

9

62

0½

306.3550

2291.0452

20

62

9 7/8

314.1600

2849.4141

20

8

68

1

322 0680

2408.5159

20

6

64

4¾

8800648

2468.3528

20

9

66

2¼

838.1687

2528.9233

Diam.

Circ.

Area in ft.

Gallons.

Ft.

In.

Ft.

In.

1 ft. in depth

21

65

11 5/8

346.3614

2590.2290

21

3

66

9

354.6571

2652.2532

21

6

67

6½

363.0511

2715.0413

21

9

68

3 7/8

371.5432

2778.5486

22

69

1 3/8

380.1336

2842.7910

22

3

69

10¾

388.8220

2907.7664

22

6

70

8¼

397.6087

2973.4889

22

9

71

5 5/8

406.4935

3039.9209

23

72

3

415.4766

3107.1001

23

3

73

0½

424.5577

3175.0122

23

6

73

9 7/8

433.7371

3243.6595

23

9

74

7¼

443.0146

3313.0403

24

75

4¾

452.3904

3383.1563

24

3

76

2 1/8

461.8642

3454.0051

24

6

76

11 5/8

471.4363

3525.5929

24

9

77

9

481.1065

3597.9068

25

78

6 3/8

490.8750

3670.9596

25

3

79

3 7/8

500.7415

3744.7452

25

6

80

1¼

510.7063

3819.2657

25

9

80

10¾

520 7692

3894.5203

26

81

8 1/8

530.9304

3970.5098

26

3

82

5¼

541.1896

4047.2322

26

6

S3

3

551.5471

4124.6893

26

9

84

0 3/8

502.0027

4202.9610

27

84

9 7/8

572.5566

4281.8072

27

3

85

8 1/8

583.2085

4361.4664

27

6

86

44

593.9587

4441.8607

27

9

87

2 1/8

604.8070

4522.9886

28

87

11½

615.7536

4604.8517

28

3

88

9

626.7982

4686.4876

28

6

89

6 3/8

637.94ll

4770.7787

28

9

90

3¾

649.1821

4854.8434

29

91

1¼

660.5214

4939.6432

29

3

91

10 5/8

671.9587

5025.1759

29

6

92

8 1/8

688.4948

5111.4487

29

9

93

5½

695.1280

5198.4451

30

94

2 7/8

706.8600

52S6.1818

80

3

95

0 3/8

718.6900

5374.6512

30

6

95

9¾

730.6183

5463.8558

80

9

96

7¼

712.6447

5553.7940