656
Molesworth’s pocket-book
Mensuration of Surfaces.
Area of triangle .. = Base X i perpendicular.
„ circle .. .. = Diameter2 X ' 7854.
„ sector of circle = Length of arc X i radius.
Number of degrees in arc X area of the circle
—
Area of parabola .. = Base X | height.
base3 — top’
Frustum of a paitabola = | height j •
Area of ellipse .. .. = Transverse axis X ’ 7s54 conjugate
axis.
= Area of generating circle X 3.
= Area of both ends + length X cir-
cumference.
„ cycloid.,
Surface of cylinder
cone .. .. = Area of base + circumference of
base X 4 slant height.
sphere .. = Diameter2 X 3’1415.
frustum .. = Sum of girt at both ends X i slant
height + area of both ends.
Segment Areas.
The area of a segment — Area of a sector — £ chord x
(radius — versin.).
Area of segment of circle = Diameter2 X ® (see Table).
V
— = The versed sine divided by the diameter of the circle
of which the segment is a part.
V D X X V X el <! y i) X
•01 ■001329 •11 •047006 •21 ■119898 •31 •207376 •41 •303187
•02 •003749 •12 •053385 •22 •128114 •32 •216666 •42 •313042
•03 •006866 •13 •059999 •23 ■136465 •33 •226034 •43 •322928
•04 •010538 ■14 •066833 •24 • 144945 •34 •235473 •44 •332843
•05 •014681 •15 •073875 •25 •153546 •35 •244980 •45 •342783
•06 •019239 •16 •081112 •26 •162263 •36 •254551 •46 ■352742
•07 ■024168 •17 •088536 •27 •171090 •37 • 264179 ■47 •362717
•08 •029435 •18 •096135 •28 •180020 •38 ■273861 •48 •372704
•09 •035012 •19 •103900 •29 •189048 •39 • 283593 •49 •382700
•10 •040875 •20 •111824 •30 •198168 •40 •293370 •50 1 •392699