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# 体积公式复习

## 棱柱和类似棱柱的几何体

${\text{体积}}_{\text{棱柱}}=\left(\text{底面积}\right)\cdot \left(\text{高}\right)$

### 长方体

$\begin{array}{rl}{\text{体积}}_{\text{长方体}}& =\left({\text{面积}}_{\text{长方形}}\right)\cdot \left(\text{高}\right)\\ \\ & =\left(\left(\text{长方形底}\right)\left(\text{长方形高}\right)\right)\cdot \left(\text{棱柱高}\right)\\ \\ & =lwh\end{array}$

### 三棱柱

$\begin{array}{rl}{\text{体积}}_{\text{三棱柱}}& =\left({\text{面积}}_{\text{三角形}}\right)\cdot \left(\text{高}\right)\\ \\ & =\left(\frac{1}{2}\left(\text{三角形底}\right)\left(\mathrm{三}\mathrm{角}\mathrm{形}\mathrm{高}\right)\cdot \left(\text{棱柱高}\right)\\ \\ & =\frac{1}{2}bh\ell \end{array}$

### 圆柱

$\begin{array}{rl}{\text{体积}}_{\text{圆柱}}& =\left({\text{面积}}_{\text{圆}}\right)\cdot \left(\text{高}\right)\\ \\ & =\left(\pi \cdot \left(\text{半径}{\right)}^{2}\right)\cdot \left(\text{高}\right)\\ \\ & =\pi {r}^{2}h\end{array}$

## 锥体和锥状体

${\text{体积}}_{\text{椎体}}=\frac{1}{3}\left(\text{底面积}\right)\cdot \left(\text{高}\right)$

### 长方锥

$\begin{array}{rl}{\text{体积}}_{\text{长方锥}}& =\frac{1}{3}\left({\text{面积}}_{\text{长方形}}\right)\cdot \left(\text{高}\right)\\ \\ & =\frac{1}{3}\left(\left(\text{长方形底}\right)\left(\text{长方形高}\right)\right)\cdot \left(\text{锥体高}\right)\\ \\ & =\frac{1}{3}lwh\end{array}$

### 圆锥

$\begin{array}{rl}{\text{体积}}_{\text{圆锥}}& =\frac{1}{3}\left({\text{面积}}_{\text{圆}}\right)\cdot \left(\text{高}\right)\\ \\ & =\frac{1}{3}\left(\pi \cdot \left(\text{半径}{\right)}^{2}\right)\cdot \left(\text{高}\right)\\ \\ & =\frac{1}{3}\pi {r}^{2}h\end{array}$

### 球体

${\text{体积}}_{\text{球体}}=\frac{4}{3}\pi \left(\text{半径}{\right)}^{3}$