Volume and Surface Area of 3D Shapes

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:

Surface Area:

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1. What is Volume and Surface Area Calculator?

Definition: This calculator computes the volume and surface area of common 3D shapes including rectangular prisms, cylinders, and spheres.

Purpose: It helps students, engineers, and professionals quickly determine the space occupied by objects and their surface coverage.

2. How Does the Calculator Work?

The calculator uses different formulas based on the selected shape:

Rectangular Prism: \[ V = L \times W \times H \] \[ SA = 2(LW + LH + WH) \]
Cylinder: \[ V = \pi r^2 h \] \[ SA = 2\pi r(r + h) \]
Sphere: \[ V = \frac{4}{3}\pi r^3 \] \[ SA = 4\pi r^2 \]

Where:

\( V \) — Volume (cubic units)
\( SA \) — Surface Area (square units)
\( L, W, H \) — Length, Width, Height (rectangular prism)
\( r \) — Radius (cylinder/sphere)
\( h \) — Height (cylinder)

3. Importance of Volume and Surface Area Calculations

Details: These calculations are essential for material estimation, container design, structural analysis, and many engineering applications.

4. Using the Calculator

Tips: Select the shape, enter the required dimensions (all must be > 0), and click Calculate. Results show both volume and surface area.

5. Frequently Asked Questions (FAQ)

Q1: What units should I use?
A: Use any consistent unit (inches, feet, meters, etc.) for all dimensions. Results will be in cubic and square units of your input.

Q2: How accurate are the calculations?
A: The calculator uses precise mathematical formulas. Accuracy depends on your input measurements.

Q3: Can I calculate for other shapes?
A: Currently supports rectangular prisms, cylinders, and spheres. More shapes may be added in future updates.

Q4: Why is surface area important?
A: Surface area determines material needed for coating, heat transfer rates, and other surface-dependent properties.

Q5: How do I measure radius for a cylinder?
A: Measure across the circular base and divide by 2. Ensure you're not entering the diameter.