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¹ÝÁö¸§ÀÌ r ÀÎ ±¸¿¡ ¹Ø¸é¿øÀÇ ¹ÝÁö¸§ÀÌ rc, ³ôÀÌ°¡ hc ÀÎ ¿ø»ÔÀÌ ±×¸²°ú °°ÀÌ ºÙ¾î ÀÖÀ» ¶§, Àüü ºÎÇǸ¦ ±¸ÇÑ´Ù.

±¸¿Í ¿ø»ÔÀÌ ¸¸³ª´Â ºÎºÐ¿¡¼­ ¿ø»ÔÀÇ ¸éÀÌ ±¸ÀÇ Á߽ɰú ÀÌ·ç´Â °¢ÀÌ ±¸ÀÇ Á¢¼± º¸´Ù Å©°Å³ª °°¾Æ¾ß ÇÑ´Ù. Áï, hm ¡Â hc ÀÌ´Ù.

±¸ÀÇ ºÎÇÇ

Vs = (4/3)*¥ð*r^3

¿ø»ÔÀÇ ºÎÇÇ

Vc = (1/3)¥ð*hc*r^2

±¸¿Í ¿ø»ÔÀÌ Áߺ¹µÈ ±íÀÌ

h = r - (r^2 - rc^2)^(1/2)

±¸¿Í ¿ø»ÔÀÌ Áߺ¹µÈ ºÎºÐÀÇ ºÎÇÇ, t = (r^2 - rc^2)^(1/2) ¶ó ÇÏ°í,

Vh = (1/3)*¥ð*h^2*(3*r-h)
   = (1/3)*¥ð*(r^2 - 2*r*t + t^2)(2*r + t)
   = (1/3)*¥ð*(2*r^3 + r^2*t - 4*r^2*t - 2*r*t^2 + 2*r*t^2 + t^3)
   = (1/3)*¥ð*(2*r^3 - 3*r^2*t + t^3)
   = (1/3)*¥ð*(2*r^3 - 3*r^2*(r^2 - rc^2)^(1/2) + (r^2 - rc^2)*(r^2 - rc^2)^(1/2))
   = (1/3)*¥ð*(2*r^3 - 2*r^2*(r^2 - rc^2)^(1/2) - rc^2*(r^2 - rc^2)^(1/2))
   = (1/3)*¥ð*(2*r^3 - (2*r^2 + rc^2)*(r^2 - rc^2)^(1/2))

µû¶ó¼­, ±¸ÇÏ°íÀÚ ÇÏ´Â ºÎÇÇ´Â

V = Vs + Vc - Vh
  = (1/3)*¥ð*(4*r^3 + hc*r^2 - 2*r^3 + (2*r^2 + rc^2)*(r^2 - rc^2)^(1/2))
  = (1/3)*¥ð*(2*r^3 + hc*r^2 + (2*r^2 + rc^2)*(r^2 - rc^2)^(1/2))

ÀÌ µÈ´Ù.

*** Âü°í¹®Çå[References] ***

V = (1/3)*¥ð*(2*r^3 + hc*r^2 + (2*r^2 + rc^2)*(r^2 - rc^2)^(1/2))
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º¯¼ö¸í Variable º¯¼ö°ª Value º¯ ¼ö ¼³ ¸í Description of the variable


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