To find the volume of a 3D figure, you typically need to use specific formulas depending on the shape of the figure. Here are some common shapes and their volume formulas:
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Cuboid (Rectangular Prism): \[ \text{Volume} = \text{length} \times \text{width} \times \text{height} \]
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Cube: \[ \text{Volume} = \text{side}^3 \]
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Cylinder: \[ \text{Volume} = \pi r^2 h \] where \( r \) is the radius of the base, and \( h \) is the height.
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Sphere: \[ \text{Volume} = \frac{4}{3} \pi r^3 \] where \( r \) is the radius.
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Cone: \[ \text{Volume} = \frac{1}{3} \pi r^2 h \] where \( r \) is the radius of the base, and \( h \) is the height.
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Pyramid: \[ \text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{height} \]
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Prism (any base shape): \[ \text{Volume} = \text{Base Area} \times \text{height} \]
To calculate the volume:
- Identify the shape of the 3D figure.
- Use the appropriate formula for that shape.
- Plug in the measurements for the dimensions (e.g., radius, height, base area).
- Perform the calculations to obtain the volume.
If the figure is irregular, you may need to divide it into simpler shapes, calculate the volume of each, and then sum them up. Alternatively, calculus techniques such as integration can be used for more complex figures.