Volumen većeg krnjeg stošca je
V 1 = v π 3 [ ( R 1 + a 2 ) 2 + ( R 1 + a 2 ) R 1 + R 1 2 ] . V_1=\frac{v\pi}{3}\left[\left(R_1+\frac a2\right)^2+\left(R_1+\frac a2\right)R_1+R_1^2\right]. V 1 = 3 v π [ ( R 1 + 2 a ) 2 + ( R 1 + 2 a ) R 1 + R 1 2 ] . Volumen manjeg krnjeg stošca je
V 2 = v π 3 [ R 1 2 + R 1 ( R 1 − a 2 ) + ( R 1 − a 2 ) 2 ] . V_2=\frac{v\pi}{3}\left[R_1^2+R_1\left(R_1-\frac a2\right)+\left(R_1-\frac a2\right)^2\right]. V 2 = 3 v π [ R 1 2 + R 1 ( R 1 − 2 a ) + ( R 1 − 2 a ) 2 ] . Volumen rotacijskog tijela je
V = V 1 − V 2 = v π 3 [ ( R 1 + a 2 ) 2 + ( R 1 + a 2 ) R 1 + R 1 2 ] − v π 3 [ R 1 2 + R 1 ( R 1 − a 2 ) + ( R 1 − a 2 ) 2 ] = a v R 1 π . \begin{aligned} V=V_1-V_2 &=\frac{v\pi}{3}\left[\left(R_1+\frac a2\right)^2+\left(R_1+\frac a2\right)R_1+R_1^2\right]\\ &\quad-\frac{v\pi}{3}\left[R_1^2+R_1\left(R_1-\frac a2\right)+\left(R_1-\frac a2\right)^2\right]\\ &=avR_1\pi. \end{aligned} V = V 1 − V 2 = 3 v π [ ( R 1 + 2 a ) 2 + ( R 1 + 2 a ) R 1 + R 1 2 ] − 3 v π [ R 1 2 + R 1 ( R 1 − 2 a ) + ( R 1 − 2 a ) 2 ] = a v R 1 π . Iz pravokutnog trokuta B C D BCD B C D
a = 2 b sin α 2 = 20 sin 15 ∘ c m , v = 10 cos 15 ∘ c m . a=2b\sin\frac\alpha2=20\sin15^\circ\,\mathrm{cm},\qquad v=10\cos15^\circ\,\mathrm{cm}. a = 2 b sin 2 α = 20 sin 1 5 ∘ cm , v = 10 cos 1 5 ∘ cm . Polumjer opisane kružnice je
R 1 = a 2 sin 30 ∘ = 20 sin 15 ∘ R_1=\frac{a}{2\sin30^\circ}=20\sin15^\circ R 1 = 2 sin 3 0 ∘ a = 20 sin 1 5 ∘ (ili R 1 = a ⋅ b ⋅ b 4 P = 20 sin 15 ∘ R_1=\frac{a\cdot b\cdot b}{4P}=20\sin15^\circ R 1 = 4 P a ⋅ b ⋅ b = 20 sin 1 5 ∘ P = 1 2 b 2 sin 30 ∘ = 25 c m 2 P=\frac12b^2\sin30^\circ=25\,\mathrm{cm}^2 P = 2 1 b 2 sin 3 0 ∘ = 25 cm 2
V = a v R 1 π = 20 sin 15 ∘ ⋅ 10 cos 15 ∘ ⋅ 20 sin 15 ∘ π = 1000 sin 15 ∘ π . V=avR_1\pi=20\sin15^\circ\cdot10\cos15^\circ\cdot20\sin15^\circ\pi=1000\sin15^\circ\pi. V = a v R 1 π = 20 sin 1 5 ∘ ⋅ 10 cos 1 5 ∘ ⋅ 20 sin 1 5 ∘ π = 1000 sin 1 5 ∘ π . sin 15 ∘ = sin ( 45 ∘ − 30 ∘ ) = 6 − 2 4 \sin15^\circ=\sin(45^\circ-30^\circ)=\frac{\sqrt6-\sqrt2}{4} sin 1 5 ∘ = sin ( 4 5 ∘ − 3 0 ∘ ) = 4 6 − 2 ili
sin 15 ∘ = sin 30 ∘ 2 = 2 − 3 2 . \sin15^\circ=\sin\frac{30^\circ}{2}=\frac{\sqrt{2-\sqrt3}}{2}. sin 1 5 ∘ = sin 2 3 0 ∘ = 2 2 − 3 . V = 250 ( 6 − 2 ) π c m 3 . V=250(\sqrt6-\sqrt2)\pi\,\mathrm{cm}^3. V = 250 ( 6 − 2 ) π cm 3 . 
