Cavalieri's Principle: Volume Formulas Argument

Sphere

Cylinder

Pyramid

Rectangular Prism

Cone

Cylinder

Pyramid

Rectangular Prism

$$V\ =5,500\ +\ 90\pi\ \cong5,782.7\ m^3$$

$$V\ =\ 5,760\ +\ 90\pi\ \cong\ 6,042.7\ m^3$$

$$V\ =\ 5,760\ +\ 360\pi\ \cong6,891\ m^3$$

$$V\ =\ 5,760\ -\ 90\pi\ \cong\ 5,477.2\ m^3$$

$$V\ =\ 594\ +\ 114.4\pi\cong\ 953.4\ mm^3$$

$$V\ =594\ -\ 114.4\pi\ \cong234.6\ mm^3$$

$$V\ =\ 594\ +\ 445.5\pi\ \cong\ 1,993.6\ mm^3$$

$$V\ =\ 594\ -\ 445.5\pi\ \cong283\ mm^3$$

$$V\ =\ 1,728\ +\ 12\pi\ \cong1,765.7\ mm^3$$

$$V\ =\ 1,728\ -\ 48\pi\ \cong\ 1,577.2\ mm^3$$

$$V\ =\ 1,728\ -12\pi\ \cong1,690.3\ mm^3$$

$$V\ =\ 1,728\ +\ 48\pi\ \cong1,878.8\ mm^3$$

$$V\ =\ 216\ -\ 8\pi\ \cong190.9\ cm^3$$

$$V\ =216\ +\ 8\pi\ \cong241.1\ cm^3$$

$$V\ =216\ +\ 96\pi\ \cong\ 517.6\ cm^3$$

$$V\ =\ 144\ -24\pi\ \cong68.6\ cm^3$$

$$225\ in^3$$

$$255\ in^3$$

$$285\ in^3$$

$$360\ in^3$$

24.6 yd^3

12.75 yd^3

27.5 yd^3

25.5 yd^2