To find the volume of an object, you measure how much space it occupies, usually in cubic units.
How to Calculate Volume
For rectangular shapes (cuboids and cubes):
- Use the formula:
Volume=length×width×height\text{Volume}=\text{length}\times \text{width}\times \text{height}Volume=length×width×height
- For a cube, since all sides are equal, multiply one side by itself three times:
V=s×s×s=s3V=s\times s\times s=s^3V=s×s×s=s3
- Example: A cuboid with length 6 cm, width 2 cm, and height 5 cm has volume:
6×2×5=60 cm36\times 2\times 5=60\text{ cm}^36×2×5=60 cm3
For compound shapes:
- Find the volume of each simple shape separately and add them together.
For other shapes:
- Cylinder:
V=πr2hV=\pi r^2hV=πr2h
- Cone:
V=13πr2hV=\frac{1}{3}\pi r^2hV=31πr2h
- Sphere:
V=43πr3V=\frac{4}{3}\pi r^3V=34πr3
Here, rrr is the radius, hhh is the height, and π≈3.14\pi \approx 3.14π≈3.14.
Units
- Volume is measured in cubic units, such as cm³, m³, or mm³.
Summary
- Measure the dimensions of the object.
- Use the appropriate volume formula depending on the shape.
- Multiply the dimensions according to the formula.
- Express the answer in cubic units.
This method applies to solids; for liquids, volume can be measured by the container or by dividing mass by density
