圓柱體積計算 上圓直徑5m 下圓直徑10m 高度2m 試問體積多少? 附上計算式 另問圓錐計算?

上圓直徑 2r = 5m

下圓直徑 2R = 10m

高度 x = 2m

V = ? m^3



1. r = 2.5 m, R = 5 m = 2r

=> h = Vertex to top plane = 2 m

=> H = h + 2 = 4 m


V = π(HR^2 - hr^2)/3

= π(4*25 - 2*6.25)/3

= 91.6 m^3




2. V = ? for general form

h/(h+x) = r/R

=> h/x = r/(R-r)

=> h = rx/(R-r)

=> H = h+x = rx/(R-r) + x = xR/(R-r)


V = π(HR^2 - hr^2)

= π(xR^3/(R-r)) - π(xr^3)/(R-r))/3

= πx/3(R-r) * (R^3 - r^3)

= πx(R^2 + Rr + r^2)/3

= 2π(25 + 5*2.5 + 6.25)/3

= 91.63 m^3



Genreal form:

V = πx(R^2 + Rr + r^2)/3