1. What are 3D Shapes Area and Volume Formulas?

Definition: These formulas calculate the space occupied (volume) and the total area of all surfaces (surface area) of three-dimensional shapes.

Purpose: Essential for geometry, engineering, architecture, and any field dealing with spatial measurements.

2. Common 3D Shape Formulas

Cube:

• Volume: \( V = s^3 \)
• Surface Area: \( SA = 6s^2 \)

Rectangular Prism:

• Volume: \( V = L \times W \times H \)
• Surface Area: \( SA = 2(LW + LH + WH) \)

Cylinder:

• Volume: \( V = \pi r^2 h \)
• Surface Area: \( SA = 2\pi r(r + h) \)

Sphere:

• Volume: \( V = \frac{4}{3}\pi r^3 \)
• Surface Area: \( SA = 4\pi r^2 \)

3. Importance of Volume and Area Calculations

Applications: Material estimation, container capacity, structural design, and scientific measurements all rely on accurate 3D calculations.

4. Using the Calculator

Steps: Select a shape, enter required dimensions (all values must be > 0), and click Calculate to get volume and surface area.

5. Frequently Asked Questions (FAQ)

Q1: What units should I use?
A: Use consistent units (all in meters, feet, etc.). Results will be in cubic units for volume and square units for area.

Q2: How precise are the calculations?
A: Results are accurate to 3 decimal places. π is approximated as 3.14159265359.

Q3: Can I calculate irregular shapes?
A: This calculator handles standard shapes only. Irregular shapes require different methods.

Q4: Why is surface area important?
A: Surface area determines material needed for covering (like paint or wrapping) and heat transfer calculations.

Q5: How do I measure dimensions accurately?
A: Use precise measuring tools and measure at multiple points for irregular objects.