aayatan

sabhi padaarth sthaan (tri-beemeeya sthaan) gherate hain. isi tri-beemeeya sthaan ki maatra ki maap ko aayatan kehte hain. ek-beemeeya aakrutiyaaain (jaise rekha) evam dvi-beemeeya aakrutiyaaain (jaise tribhuj, chaturbhuj, varg aadi) ka aayatan shoonya hota hai.

anukram

aayatan ke sootr

aayatan ke pramukh sameekaran:
aakaar sootr char (Variables) ka arth
ghan (cube): s = ek bhuja ki lambaai
ghanaabh (pairelopaaipd) : l = lambaai, w = chaudaai, h = ooainchaai
lamb vrutteeya belan (ya, vrutteeya prijm) : r = samatal vrutteeya falak (face) ki trijya, h = ooainchaai
koi bhi prijm, jiski poori ooainchaai mein sarvatr anuprasth kaat ka kshetrafal samaan ho**: A = aadhaar ka kshetrafal, h = oonchaai
gola (sphere)
gole ka aayatan uske vakr prusht ke samaakalan (inteegreshan) ke baraabar hota hai.
r = gole ki trijya
deergh vruttaabh (ellipsoid): a, b, c = deergh vruttaabh ke ardhaaksh (semi-axes) ki maap
soochi stambh (Pyramid): A = aadhaar ka kshetrafal, h = lambavat ooainchaai
shanku (Cone) ya vrutteeya aadhaar wala soochi-stambh (pyramid): r = vrutteeya aadhaar ki trijya, h = sheersh (tip) ki aadhaar se lambavat doori
kisi bhi aakaar ke liye (samaakalan ka prayog karna padta hai) h = aakruti ka koi beema (dimension), A(h) = h ke lambavat kshetrafal

(aayatan ki ikaai ghan meter', ghan semi, liter aadi hoti hain.

kisi ghanaabh ke aayatan ke liye sadish (vektar) sootr :

kisi ghanaabh ke kisi ek sheersh par milne waali teenon kor () ko sadish roop mein vyakt karein to usaka aayatan in teen sadishon ke adish gunanafal (scalar triple product) ke baraabar hota hai.

kisi chatushfalaki (tetrahedron) ke aayatan ke liye sadish sootr :

kisi chatushfalaki ke chaaro sheershon ke sthiti sadish (position vectors) a, b, c and d hon to usaka aayatan (ab, bc, cd) ke tiryak sadish gunanafal (scalar triple product) ke 1/6 ke baraabar hota hai.

aayatan aur ghanatv (density)

kisi padaarth ke ikaai aayatan mein nihit drabyamaan (mass) ko us padaarth ka ghanatv kehte hain. lohe ka ghanatv lakdi ke ghanatv se adhik hota hai.

inhein bhi dekhein

baahari kadiyaaain