Volume of 3D Shapes Corbettmaths

Volume Formulas:

\[ V = L \times W \times H \text{ (rectangular)} \] \[ V = \pi \times r^2 \times h \text{ (cylindrical)} \]

Select Shape:

Length:

units

Width:

units

Height:

units

Volume:

cubic units

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1. What is Volume of 3D Shapes?

Definition: Volume is the amount of space occupied by a three-dimensional object, measured in cubic units.

Purpose: Calculating volume is essential in mathematics, engineering, construction, and many real-world applications.

2. How Does the Calculator Work?

The calculator uses different formulas based on the selected shape:

\[ \text{Rectangular Prism: } V = L \times W \times H \] \[ \text{Cylinder: } V = \pi \times r^2 \times h \] \[ \text{Sphere: } V = \frac{4}{3} \times \pi \times r^3 \]

Where:

\( V \) — Volume (cubic units)
\( L \) — Length (units)
\( W \) — Width (units)
\( H \) — Height (units)
\( r \) — Radius (units)
\( h \) — Height (units)
\( \pi \) — Pi (approximately 3.14159)

3. Importance of Volume Calculation

Details: Volume calculations are fundamental in:

Determining material quantities for construction
Calculating container capacities
Solving physics and engineering problems
Many everyday applications like cooking and packaging

4. Using the Calculator

Tips:

Select the shape you want to calculate
Enter the required dimensions (all must be positive numbers)
Click "Calculate" to get the volume
All measurements must be in the same units

5. Frequently Asked Questions (FAQ)

Q1: What units should I use?
A: You can use any units (meters, feet, inches, etc.) as long as all dimensions use the same unit.

Q2: How accurate is the calculation?
A: The calculator uses precise mathematical formulas and displays results to 3 decimal places.

Q3: Can I calculate volume for irregular shapes?
A: This calculator is for regular shapes only. Irregular shapes require different methods.

Q4: What's the difference between volume and surface area?
A: Volume measures space inside, while surface area measures the total outside area.

Q5: Why is π used in cylinder and sphere formulas?
A: π relates a circle's circumference to its diameter, essential for circular-based shapes.