圓錐體積計算

圓錐
圓錐

計算結果

體積

重量

圓錐體積

\[ \displaystyle \begin{aligned} &= \frac{1}{3} \times \text{底圓面積} \times \text{錐高}\\[6pt] &= \frac{1}{3} \times \text{圓周率} (\cong 3.1415926) × \text{半徑}^2 × \text{錐高} \\[6pt] &= \frac{1}{12} \times \text{圓周率} × \text{直徑}^2 × \text{錐高} \\[6pt] &= \frac{1}{12} \; \pi D^2 H \\[6pt] \end{aligned} \]

圓錐體積

\[ \displaystyle \begin{aligned} &= \frac{1}{3} \times \text{底圓面積} \times \text{錐高}\\[6pt] &= \frac{1}{3} \times \text{圓周率} (\cong 3.1415926) × \text{半徑}^2 × \text{錐高} \\[6pt] &= \frac{1}{12} \times \text{圓周率} × \text{直徑}^2 × \text{錐高} \\[6pt] &= \frac{1}{12} \times \text{圓周率} × \text{直徑}^2 × \left[ \frac{\text{直徑}}{2} × cot \left( \frac{\text{錐角}}{2} \right) \right] \\[6pt] &= \frac{1}{24} \; \pi D^3 cot \left( \frac{A}{2} \right) \\[6pt] \end{aligned} \]