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Mathematical formula for calculating surface area and volume
The circumference of a rectangle = (length+width) ×2

Circumference of a square = side length ×4

Area of rectangle = length × width

Area of a square = side length × side length

Area of triangle = base × height ÷2

Area of parallelogram = base × height

Trapezoidal area = (upper bottom+lower bottom) × height ÷2

Diameter = radius ×2

Radius = Diameter ÷2

Circumference = π× diameter =

Pi× radius× 2

Area of circle = π× radius× radius

Surface area of cuboid =

(length× width+length× height+width× height) ×2

Volume of cuboid

= length × width × height

Surface area of cube = side length × side length ×6

Volume of cube = side length × side length × side length

Lateral area of cylinder = perimeter of bottom circle × height.

Surface area of cylinder = upper and lower bottom area+side area.

Volume of cylinder = bottom area × height

Volume of cone = 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

Height of h-a edge

Half the circumference

A, b, c- internal angle

Where 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

Height of h-a side

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- centerline 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

Degree of α -central angle

s = R2/2(ωα/ 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

S- bottom area

S-side-lateral area

S table-surface area

C=2πr

S bottom = π R2

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 the center of the circle is the center of the bucket)

V=πh(2D2+Dd+3d2/4)/ 15

(The bus is a parabola)