Cylindrical surface area = upper and lower bottom surface area+side surface area.
Cylinder volume = bottom area × height
Cone volume = bottom area × height ÷3
Cuboid (cube, cylinder)
Volume = bottom area × height
plane graph
name
sign
Perimeter c and area s
square
Length of side a
C=4a
S=a2
rectangle
Length of side a and side b
C=2(a+b)
S=ab
triangle
A, b, c- trilateral length
H-a side height
S- half the circumference
A, b, C- internal angle
Its s=(a+b+c)/2.
S=ah/2
=ab/2？ sinC
=[s(s-a)(s-b)(s-c)] 1/2
=a2sinBsinC/(2sinA)
quadrilateral
D, D- diagonal length
α diagonal
S=dD/2？ sinα
parallelogram
Length of a and b sides
H-a side height
Alpha angle between two sides
S = ah
=absinα
diamond
Length of side a
α-included angle
D- long diagonal length
D- short diagonal length
S=Dd/2
=a2sinα
trapeziform
A and b- the length of the upper and lower bottoms
up level
M bit line length
S=(a+b)h/2
=mh
circle
R radius
diameter
C=πd=2πr
S=πr2
=πd2/4
department
R- sector radius
Degree of central angle
C=2r+2πr×(a/360)
S=πr2×(a/360)
arch form
L- arc length
B chord length
H vector height
R radius
α degree of central angle
S=r2/2？ (πα/ 180-sinα)
=r2arccos[(r-h)/r]
-
(r-h)(2rh-h2) 1/2
=παr2/360
-
b/2？ [r2-(b/2)2] 1/2
=r(l-b)/2
+
bh/2
≈2bh/3
ring
R- excircle radius
R- radius of inner circle
D- cylinder diameter
Diameter of inner circle
S=π(R2-r2)
=π(D2-d2)/4
oblong
D long axis
D- minor axis
S=πDd/4
Cubic figure
name
sign
Area s and volume v
cube
Length of side a
S=6a2
V=a3
Cubic
Achang
B width
C height adjustment
S=2(ab+ac+bc)
V=abc
prism
S- bottom area
up level
V=Sh
pyramid
S- bottom area
up level
V=Sh/3
frustum of a pyramid
S 1 and S2- upper and lower bottom areas
up level
v = h[s 1+S2+(s 1s 1) 1/2]/3
Prismatic
S 1- upper bottom area
S2- bottom area
S0- Cross-sectional area
up level
V=h(S 1+S2+4S0)/6
column
R- bottom radius
up level
Bottom circumference
Bottom-bottom region
S-side-lateral area
S table-surface area
C=2πr
S bottom =πr2
S side =Ch
S table =Ch+2S bottom
V=S bottom h
=πr2h
Hollow cylinder
R- excircle radius
R- radius of inner circle
up level
V=πh(R2-r2)
Straight cone
R- bottom radius
up level
V=πr2h/3
Circular truncated cone
R- upper bottom radius
R- bottom radius
up level
V=πh(R2+Rr+r2)/3
ball
R radius
diameter
V=4/3πr3=πd2/6
Bulb deficiency
H-ball missing height
R sphere radius
A- the radius of the missing bottom of the ball
V=πh(3a2+h2)/6
=πh2(3r-h)/3
a2=h(2r-h)
table
R 1 and r2- the radius of the top and bottom of the table.
up level
V=πh[3(r 12+r22)+h2]/6
receptacle
R-ring radius
D-ring diameter
R-ring section radius
D- ring section diameter
V=2π2Rr2
=π2Dd2/4
staving
D- drum belly diameter
D- barrel bottom diameter
H- barrel height
V=πh(2D2+d2)/ 12
(The bus is circular and centered on the cylinder)
V=πh(2D2+Dd+3d2/4)/ 15