ื ืคื— ื•ืฉื˜ื— ืคื ื™ื: ื ืคื— ืชื™ื‘ื”

ืœืžื“ื• ื›ื™ืฆื“ ืœื—ืฉื‘ ื ืคื— ืฉืœ ืชื™ื‘ื•ืช, ืงื•ื‘ื™ื•ืช, ื’ื•ืคื™ื ืžื•ืจื›ื‘ื™ื ื•ืชื™ื‘ื•ืช ืขื ื—ื™ืชื•ื›ื™ื. ืชืจื’ื•ืœ ืื™ื ื˜ืจืืงื˜ื™ื‘ื™ ืขื ื”ืกื‘ืจื™ื ืžืคื•ืจื˜ื™ื ืฉืœื‘ ืื—ืจ ืฉืœื‘.

ืชืจื’ื•ืœ

๐Ÿ“– ืžื“ืจื™ืš ืœืžื™ื“ื”

ื ืคื— ื”ื•ื ื›ืžื•ืช ื”ืžืจื—ื‘ ื”ืชืœืช-ืžืžื“ื™ ื”ื›ืœื•ื ื‘ืชื•ืš ื’ื•ืฃ ืกื’ื•ืจ. ื”ื•ื ืžื•ื“ื“ ื›ืžื” ืžืงื•ื ืชื•ืคืก ื”ื’ื•ืฃ, ื•ื ืžื“ื“ ื‘ื“ืจืš ื›ืœืœ ื‘ื™ื—ื™ื“ื•ืช ืžืขื•ืงื‘ื•ืช (ื›ืžื• ืกืžืดืง ืื• ืžืดืง).

1. ื ืคื— ืชื™ื‘ื”

ืœืชื™ื‘ื” ื™ืฉ ืฉืœื•ืฉื” ืžืžื“ื™ื ืขื™ืงืจื™ื™ื: ืื•ืจืš ll, ืจื•ื—ื‘ ww ื•ื’ื•ื‘ื” hh. ื”ื ืคื— ืžื—ื•ืฉื‘ ืขืœ ื™ื“ื™ ืžื›ืคืœืช ืฉืœื•ืฉืช ื”ืžืžื“ื™ื ื”ืœืœื•:
V=lร—wร—hV = l \times w \times h

ืžืฉืชื ื™ื:
โ€ข VV = ื ืคื—
โ€ข ll = ืื•ืจืš ื”ืชื™ื‘ื”
โ€ข ww = ืจื•ื—ื‘ ื”ืชื™ื‘ื”
โ€ข hh = ื’ื•ื‘ื” ื”ืชื™ื‘ื”

ื”ืกื‘ืจ: ื”ื ื•ืกื—ื” ืžื—ืฉื‘ืช ืืช ืฉื˜ื— ื‘ืกื™ืก ื”ืชื™ื‘ื” (lร—wl \times w) ื•ื›ื•ืคืœืช ืื•ืชื• ื‘ื’ื•ื‘ื” (hh) ื›ื“ื™ ืœื”ืจื—ื™ื‘ ืืช ื”ืžืฉื˜ื— ื”ื“ื•-ืžืžื“ื™ ืœืžืจื—ื‘ ืชืœืช-ืžืžื“ื™.

2. ืงื•ื‘ื™ื™ื” ื›ืžืงืจื” ืคืจื˜ื™ ืฉืœ ืชื™ื‘ื”

ืงื•ื‘ื™ื™ื” ื”ื™ื ืžืงืจื” ืคืจื˜ื™ ืฉืœ ืชื™ื‘ื” ืฉื‘ื• ื›ืœ ืฉืœื•ืฉืช ื”ืžืžื“ื™ื ืฉื•ื•ื™ื ื–ื” ืœื–ื” (ืื•ืจืš = ืจื•ื—ื‘ = ื’ื•ื‘ื” = ss). ืื ื ืฆื™ื‘ l=sl=s, w=sw=s, ื•-h=sh=s ื‘ื ื•ืกื—ืช ื”ืชื™ื‘ื”, ื ืงื‘ืœ:
V=sร—sร—s=s3V = s \times s \times s = s^3

ืžืฉืชื ื™ื:
โ€ข VV = ื ืคื—
โ€ข ss = ืื•ืจืš ืฆืœืข ื”ืงื•ื‘ื™ื™ื”

3. ื’ื•ืคื™ื ืžื•ืจื›ื‘ื™ื ื•ื’ืจื™ืขื•ืช (ื—ื™ืชื•ื›ื™ื)

ื›ื“ื™ ืœื—ืฉื‘ ื ืคื— ืฉืœ ื’ื•ืคื™ื ืžื•ืจื›ื‘ื™ื ื™ื•ืชืจ, ื ืฉืชืžืฉ ื‘ืคืขื•ืœื•ืช ื—ื™ื‘ื•ืจ ื•ื—ื™ืกื•ืจ:

ื ืคื— ื’ื•ืคื™ื ืžื•ืจื›ื‘ื™ื

Vืกืšย ื”ื›ืœ=V1+V2+โ€ฆV_{\text{ืกืš ื”ื›ืœ}} = V_1 + V_2 + \dots
ื›ืืฉืจ ืชื™ื‘ื•ืช ืฆืžื•ื“ื•ืช ื–ื• ืœื–ื• ืื• ืžื•ื ื—ื•ืช ื–ื• ืขืœ ื’ื‘ื™ ื–ื•, ื”ื ืคื— ื”ื›ื•ืœืœ ื”ื•ื ืกื›ื•ื ื”ื ืคื—ื™ื ืฉืœ ื”ืชื™ื‘ื•ืช ื”ื‘ื•ื“ื“ื•ืช.

ืขื‘ื•ืจ ื’ื•ืคื™ื ืขื ื—ืœืœื™ื, ื—ื•ืจื™ื ืื• ื’ืจื™ืขื•ืช, ื ื—ืกื™ืจ ืืช ื”ื ืคื—ื™ื:

ื ืคื— ื’ืจื™ืขื•ืช ื•ื—ื•ืจื™ื

Vื ื•ืชืจ=Vื—ื™ืฆื•ื ื™โˆ’Vืคื ื™ืžื™V_{\text{ื ื•ืชืจ}} = V_{\text{ื—ื™ืฆื•ื ื™}} - V_{\text{ืคื ื™ืžื™}}
ืื ื ื’ืจืขืช ืชื™ื‘ื” ืงื˜ื ื” ืžืชื•ืš ืชื™ื‘ื” ื’ื“ื•ืœื”, ื”ื ืคื— ื”ื ื•ืชืจ ื”ื•ื ื ืคื— ื”ืชื™ื‘ื” ื”ื—ื™ืฆื•ื ื™ืช ืคื—ื•ืช ื ืคื— ื”ื’ืจื™ืขื” ื”ืคื ื™ืžื™ืช.
ื ื•ืฉืื™ ืœื™ืžื•ื“

ืฉืืœื•ืช ื ืคื•ืฆื•ืช

ืžื”ื• ื ืคื—?

ื ืคื— ื”ื•ื ืžื™ื“ืช ื”ืžืจื—ื‘ ื”ืชืœืช-ืžืžื“ื™ ืฉืชื•ืคืก ื’ื•ืฃ ื›ืœืฉื”ื•. ื”ื•ื ื ืžื“ื“ ื‘ื™ื—ื™ื“ื•ืช ื ืคื— ืžืขื•ืงื‘ื•ืช, ื›ื’ื•ืŸ ืกื ื˜ื™ืžื˜ืจ ืžืขื•ืงื‘ (ืกืž"ืง) ืื• ืžื˜ืจ ืžืขื•ืงื‘ (ืž"ืง).

ื›ื™ืฆื“ ืžื—ืฉื‘ื™ื ื ืคื— ืฉืœ ืชื™ื‘ื”?

ื ืคื— ืฉืœ ืชื™ื‘ื” ืžื—ื•ืฉื‘ ืขืœ ื™ื“ื™ ืžื›ืคืœืช ื”ืื•ืจืš, ื”ืจื•ื—ื‘ ื•ื”ื’ื•ื‘ื” ืฉืœื”: V = l ร— w ร— h.

ื ืคื— ืชื™ื‘ื” ื•ืงื•ื‘ื™ื™ื” โ€” ืžื“ืจื™ืš ื•ืชืจื’ื•ืœ | SealMath