Cylinder:
Surface area: 2πRr+2πRh Volume: πRRh (R is the radius of the upper and lower bottom circles of the cylinder, and H is the height of the cylinder)
Cone:
Surface area: π RR+π R [square root of (hh+RR)] Volume: πRRh/3 (r is the radius of the cone's low circle, and H is its height,
2 plane graphics
Name symbol perimeter c and area s
The length of side a of a square is c = 4as = a2.
The length of a side and b side of a rectangle C = 2 (A+B) S = AB.
Triangle a, b, C- has three sides, H-A, height S- half of the circumference, a, b, C- inner angle, among which
S =(a+b+c)/2s = ah/2 = ab/2 sinC =[S(S-a)(S-b)(S-c)] 1/2 = a2 sinbsinc/(2 Sina)
Quadrilateral d, D- diagonal length α-diagonal angle S = d, D-/2 sin α
Parallelogram a, b- side length h- side height α-included angle s = ah = absin α.
Diamond A- side length α-included angle D- long diagonal length D- short diagonal length S = DD/2 = A2Sinα
Trapezoids a and b- upper and lower base length h- height m- midline length s = (a+b) h/2 = MH.
Circle r- radius d- diameter c = π d = 2π rs = π R2 = π d2/4.
Sector r- sector radius a- degree of central angle c = 2r+2π r× (a/360) s = π R2× (a/360)
Bow L- arc length S = R2/2 (π α/ 180-sin α)
B chord length = R2arccos [(r-h)/r]-(r-h) (2RH-H2)1/2.
H vector height = π α R2/360-b/2 [R2-(b/2) 2]1/2.
R- radius = r (l-b)/2+BH/2.
Degree of α-central angle ≈2bh/3
Ring r- excircle radius s = π (R2-R2)
R- radius of inner circle = π (D2-D2)/4
D- cylinder diameter
Diameter of inner circle
Ellipse d- major axis s = π DD/4
D- minor axis
3 supplementary edition
plane graph
Name symbol
Perimeter c and area s
The length of side a of a square is c = 4a.
S=a^2
rectangle
The length of side a and side b is c = 2 (a+b).
S=ab
triangle
A, b, C- trilateral length
Height of h-a edge
Half the circumference
A, b, c- internal angle
Where s = (a+b+c)/2s = ah/2.
=ab/2 sinC
=[s(s-a)(s-b)(s-c)] 1/2
=a^2sinBsinC/(2sinA)
quadrilateral
D, d- diagonal length
α diagonal angle s = DD/2 sin α
parallelogram
Length of a and b sides
Height of h-a side
α-included 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
=a^2sinα
trapeziform
A and b- the length of the upper and lower bottoms
up level
M- centerline length s = (a+b) h/2
=mh
circle
R radius
D- diameter c = π d = 2π r
S=πr^2
=πd^2/4
department
R- sector radius
Degree of central angle
C=2r+2πr×(a/360)
S=πr^2×(a/360)
arch form
L- arc length
B chord length
H vector height
R radius
The degree of α-central angle s = r 2/2 (π α/ 180-sin α)
=r^2arccos[(r-h)/r——(r-h)(2rh-h^2) 1/2
=παr^2/360-b/2[r^2-(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
D- diameter of inner circle s = π (r 2-r 2)
=π(D^2-d^2)/4
oblong
D long axis
D- minor axis s = π DD/4
Cubic figure
Name symbol
Area s and volume v
The side length of cube a is s = 6a 2.
V=a^3
Cubic
Achang
B width
C- height s = 2 (AB+AC+BC)
V=abc
prism
S- bottom area
H- height v = sh
pyramid
S- bottom area
H- height v = sh/3
frustum of a pyramid
S 1 and S2- upper and lower bottom areas
H- height v = h [s1+S2+(s1S2)1/2]/3.
Prismatic
S 1- upper bottom area
S2- bottom area
S0- Cross-sectional area
H- height v = h (s 1+S2+4s0)/6.
column
R- bottom radius
up level
Bottom circumference
S- bottom area
S-side-lateral area
S table-surface area c = 2π r
S base = π r 2
S side = ch
S table = ch+2s bottom
V = s bottom h
=πr^2h
Hollow cylinder
R- excircle radius
R- radius of inner circle
H- height v = π h (r 2-r 2)
Straight cone
R- bottom radius
H- height v = π r 2h/3
Circular truncated cone
R- upper bottom radius
R- bottom radius
H- height v = π h (r 2+RR+r 2)/3
ball
R radius
D- diameter v = 4/3 π r 3 = π d 3/6
Bulb deficiency
H-ball missing height
R sphere radius
A- Radius of ball bottom v = π h (3a 2+h 2)/6.
=πh^2(3r-h)/3
a2=h(2r-h)
table
R 1 and R2- the radius of the top and bottom of the table.
H- height v = π h [3 (r 1 2+R2 2)+h 2]/6.
receptacle
R-ring radius
D-ring diameter
R-ring section radius
D-ring section diameter v = 2π 2rr 2
=π2Dd^2/4
staving
D- drum belly diameter
D- barrel bottom diameter
H- barrel height v = π h (2d 2+d 2)/ 12.
(The bus is circular, and the center of the circle is the center of the bucket)
V=πh(2D^2+Dd+3d^2/4)/ 15
(The bus is a parabola) References:
/blog/static/6708396220092263121/
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Cuboid:
Surface area: 2(ab+ah+bh)
Volume: abh(a is the length of the cuboid, b is the width of the cuboid, and h is the height of the cuboid)
Cube:
Surface area: 6a^2
Volume: A 3 (A is the side length of the cube)
Cylinder:
Surface area: 2π r 2+2π rh
Volume: π r 2h (R is the radius of the upper and lower bottom circles of the cylinder, and H is the height of the cylinder)
Cone:
Surface area: π r 2+π r radical (H 2+R 2)
Volume: π r 2h/3 (R is the radius of the cone's low circle and H is its height)
Surface area of regular prism and regular pyramid
Let the height of the prism be h and the perimeter of the bottom polygon be c, then the lateral area formula of the right-angled prism is: s right-angled prism lateral area = CH.
That is to say, the side area of a right-angled prism is equal to the product of its bottom perimeter and height.
Let the side length of the bottom surface of a regular pyramid be a, the perimeter of the bottom surface be c, and the inclined height be h', then the lateral area formula of the regular pyramid is:
Right side of the pyramid = nah' = ch'
That is to say, the side area of a regular pyramid is equal to half of the product of the perimeter of its bottom surface and the oblique height.
The surface area or total area of prism and pyramid is equal to the sum of lateral area and base area.
Prism surface area
Let the side length of the lower bottom surface of the prism be a, the perimeter of the prism be c, the side length of the upper bottom surface be a', the perimeter be c', and the inclined height be h', then the formula of the side area of the regular prism can be obtained.
S prism edge = n(a+a')h'=(c+c')h'
The surface area or total area of a prism is equal to the sum of the side area and the bottom area.
Go and see here.
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